Identifier
-
Mp00152:
Graphs
—Laplacian multiplicities⟶
Integer compositions
St000382: Integer compositions ⟶ ℤ
Values
=>
Cc0020;cc-rep-0
([],1)=>[1]=>1
([],2)=>[2]=>2
([(0,1)],2)=>[1,1]=>1
([],3)=>[3]=>3
([(1,2)],3)=>[1,2]=>1
([(0,2),(1,2)],3)=>[1,1,1]=>1
([(0,1),(0,2),(1,2)],3)=>[2,1]=>2
([],4)=>[4]=>4
([(2,3)],4)=>[1,3]=>1
([(1,3),(2,3)],4)=>[1,1,2]=>1
([(0,3),(1,3),(2,3)],4)=>[1,2,1]=>1
([(0,3),(1,2)],4)=>[2,2]=>2
([(0,3),(1,2),(2,3)],4)=>[1,1,1,1]=>1
([(1,2),(1,3),(2,3)],4)=>[2,2]=>2
([(0,3),(1,2),(1,3),(2,3)],4)=>[1,1,1,1]=>1
([(0,2),(0,3),(1,2),(1,3)],4)=>[1,2,1]=>1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[2,1,1]=>2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[3,1]=>3
([],5)=>[5]=>5
([(3,4)],5)=>[1,4]=>1
([(2,4),(3,4)],5)=>[1,1,3]=>1
([(1,4),(2,4),(3,4)],5)=>[1,2,2]=>1
([(0,4),(1,4),(2,4),(3,4)],5)=>[1,3,1]=>1
([(1,4),(2,3)],5)=>[2,3]=>2
([(1,4),(2,3),(3,4)],5)=>[1,1,1,2]=>1
([(0,1),(2,4),(3,4)],5)=>[1,1,1,2]=>1
([(2,3),(2,4),(3,4)],5)=>[2,3]=>2
([(0,4),(1,4),(2,3),(3,4)],5)=>[1,1,1,1,1]=>1
([(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,1,2]=>1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,2,1]=>1
([(1,3),(1,4),(2,3),(2,4)],5)=>[1,2,2]=>1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,2]=>2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>[1,1,2,1]=>1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,2,1]=>2
([(0,4),(1,3),(2,3),(2,4)],5)=>[1,1,1,1,1]=>1
([(0,1),(2,3),(2,4),(3,4)],5)=>[2,1,2]=>2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>[1,2,1,1]=>1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>[2,2,1]=>2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>[1,1,1,1,1]=>1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,2]=>3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[1,2,1,1]=>1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[2,1,1,1]=>2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>[1,1,1,1,1]=>1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>[2,2,1]=>2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[3,1,1]=>3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[4,1]=>4
([],6)=>[6]=>6
([(4,5)],6)=>[1,5]=>1
([(3,5),(4,5)],6)=>[1,1,4]=>1
([(2,5),(3,5),(4,5)],6)=>[1,2,3]=>1
([(1,5),(2,5),(3,5),(4,5)],6)=>[1,3,2]=>1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>[1,4,1]=>1
([(2,5),(3,4)],6)=>[2,4]=>2
([(2,5),(3,4),(4,5)],6)=>[1,1,1,3]=>1
([(1,2),(3,5),(4,5)],6)=>[1,1,1,3]=>1
([(3,4),(3,5),(4,5)],6)=>[2,4]=>2
([(1,5),(2,5),(3,4),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,1),(2,5),(3,5),(4,5)],6)=>[1,1,2,2]=>1
([(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,3]=>1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>[1,1,2,1,1]=>1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,2,2]=>1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,3,1]=>1
([(2,4),(2,5),(3,4),(3,5)],6)=>[1,2,3]=>1
([(0,5),(1,5),(2,4),(3,4)],6)=>[2,2,2]=>2
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,3]=>2
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,2,1]=>1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,2,2]=>1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,2,1,1]=>1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,3,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,3,1]=>2
([(0,5),(1,4),(2,3)],6)=>[3,3]=>3
([(1,5),(2,4),(3,4),(3,5)],6)=>[1,1,1,1,2]=>1
([(0,1),(2,5),(3,4),(4,5)],6)=>[1,2,1,2]=>1
([(1,2),(3,4),(3,5),(4,5)],6)=>[2,1,3]=>2
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[1,2,1,2]=>1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[1,2,2,1]=>1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>[2,2,2]=>2
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>[2,1,2,1]=>2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>[1,3,2]=>1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>[3,1,2]=>3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>[1,2,1,1,1]=>1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,2]=>2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,3]=>3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,2]=>1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,2,1]=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,2,1,1]=>1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,2]=>2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,2,2,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,2,1]=>2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,2]=>1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,2,2]=>2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>[1,2,2,1]=>1
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,3,1,1]=>1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,2]=>3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[2,1,2,1]=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>[1,4,1]=>1
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,3,1]=>1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,1,2,1]=>2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>[4,2]=>4
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>[1,3,1,1]=>1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,2]=>3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[1,3,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,2,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>[1,2,2,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>[2,2,1,1]=>2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,1,1,1,1]=>2
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,1,1,1]=>1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,2]=>4
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,3,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[2,2,1,1]=>2
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,1,1,1]=>3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,1,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>[1,2,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[1,2,2,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>[2,1,1,1,1]=>2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>[2,3,1]=>2
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[3,2,1]=>3
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[4,1,1]=>4
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>[5,1]=>5
([],7)=>[7]=>7
([(5,6)],7)=>[1,6]=>1
([(4,6),(5,6)],7)=>[1,1,5]=>1
([(3,6),(4,6),(5,6)],7)=>[1,2,4]=>1
([(2,6),(3,6),(4,6),(5,6)],7)=>[1,3,3]=>1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[1,4,2]=>1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>[1,5,1]=>1
([(3,6),(4,5)],7)=>[2,5]=>2
([(3,6),(4,5),(5,6)],7)=>[1,1,1,4]=>1
([(2,3),(4,6),(5,6)],7)=>[1,1,1,4]=>1
([(4,5),(4,6),(5,6)],7)=>[2,5]=>2
([(2,6),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,2),(3,6),(4,6),(5,6)],7)=>[1,1,2,3]=>1
([(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,4]=>1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,3,2]=>1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,3]=>1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>[1,1,3,1,1]=>1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,3,2]=>1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,4,1]=>1
([(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,4]=>1
([(1,6),(2,6),(3,5),(4,5)],7)=>[2,2,3]=>2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>[1,1,3,2]=>1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,4]=>2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[1,1,2,1,2]=>1
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,2]=>1
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,3,1]=>1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,3]=>1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,3]=>2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,2,1]=>1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,3,2]=>1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,3,1,1]=>1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,3,2]=>2
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,4,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,4,1]=>2
([(1,6),(2,5),(3,4)],7)=>[3,4]=>3
([(2,6),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,3]=>1
([(1,2),(3,6),(4,5),(5,6)],7)=>[1,2,1,3]=>1
([(0,3),(1,2),(4,6),(5,6)],7)=>[1,2,1,3]=>1
([(2,3),(4,5),(4,6),(5,6)],7)=>[2,1,4]=>2
([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,2]=>1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,3]=>1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,2,2]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,3,1]=>1
([(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[2,2,3]=>2
([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[2,1,2,2]=>2
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,3]=>1
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,2,1]=>1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,3]=>1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[3,1,3]=>3
([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,2]=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[1,2,2,2]=>1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,3]=>2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,2,1]=>1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7)=>[1,2,2,2]=>1
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,4]=>3
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,3]=>1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,2]=>1
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,3,1]=>1
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,3,2]=>1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,3,2]=>2
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,3]=>2
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,2,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,2,2]=>1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,2]=>2
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,3,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,3,1]=>2
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,3]=>1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,3]=>2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,2,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,6),(4,5)],7)=>[1,2,2,2]=>1
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>[1,1,2,1,2]=>1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[2,1,1,1,2]=>2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,1,2]=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,2]=>1
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7)=>[2,1,2,1,1]=>2
([(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,3]=>3
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,1,2,2]=>2
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,2,1]=>2
([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,2]=>2
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,2,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,2,1]=>2
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[1,4,2]=>1
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,3,2]=>1
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,1,2,2]=>2
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>3
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,2,1]=>2
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(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)=>[1,2,3,1]=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,3,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,1,3,1]=>2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>3
([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7)=>[2,2,3]=>2
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,3,2,1]=>1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[2,1,2,2]=>2
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7)=>[4,3]=>4
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,3,1,2]=>1
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7)=>[1,3,1,2]=>1
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,3]=>3
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,2]=>1
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,2,1,2]=>1
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,2]=>2
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,1,2]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,2]=>2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,2,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>2
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7)=>[2,2,2,1]=>2
([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,2]=>1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,2,2]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,5),(2,3),(2,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[2,2,1,2]=>2
([(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)=>[3,3,1]=>3
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6)],7)=>[1,2,1,2,1]=>1
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,2]=>1
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,2]=>1
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,2]=>2
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,2]=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,2),(1,4),(1,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,1,2]=>2
([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(2,3),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,2]=>3
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7)=>[1,2,2,2]=>1
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,2]=>3
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,2]=>2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,3]=>4
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,2]=>1
([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,2,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,2]=>2
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,2,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>2
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(4,5)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,4),(1,2),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,4),(0,5),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,4),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,2]=>1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,2]=>1
([(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,2]=>1
([(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,1,1,1,2]=>2
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,2]=>3
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,2,1]=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,2,1]=>2
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,2,1]=>3
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[2,3,2]=>2
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>3
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,2,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6)],7)=>[1,2,1,2,1]=>1
([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,2,2,1]=>1
([(0,4),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,3),(1,5),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,3),(0,6),(1,2),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7)=>[1,2,1,2,1]=>1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,1),(0,4),(0,6),(1,2),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,4),(1,3),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(1,3),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,1),(0,2),(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,2),(0,6),(1,2),(1,4),(1,5),(2,3),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,2]=>4
([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[3,3,1]=>3
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,5),(1,4),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,4),(0,5),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,3),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>3
([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[1,1,2,2,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,6),(4,6),(5,6)],7)=>[2,4,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>[1,2,2,1,1]=>1
([(0,2),(0,3),(0,4),(0,6),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,1),(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,3,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[2,2,2,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,2,1]=>3
([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>4
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,2]=>3
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,4,1,1]=>1
([(0,1),(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,3),(0,6),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,3,1,1]=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,2]=>4
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,1),(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,1,1,1]=>2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(1,3),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,2,1,1]=>1
([(0,1),(0,3),(0,4),(1,2),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,3),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,1),(0,2),(0,3),(0,4),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,2,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,3,1,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>3
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,6),(1,3),(1,5),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[1,2,1,2,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>2
([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>[1,2,1,2,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7)=>[1,2,2,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>[2,2,2,1]=>2
([(0,1),(0,3),(0,4),(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,5),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,2),(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,1,2,1,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>3
([(0,2),(0,3),(0,6),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,1,1,1,1,1]=>2
([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,1,2,1,1,1]=>1
([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,2]=>5
([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,4,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,3,1,1]=>2
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,2,1,1]=>3
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,1,1,1]=>4
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7)=>[1,3,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[1,3,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[2,2,1,1,1]=>2
([(0,1),(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[2,2,2,1]=>2
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[3,1,1,1,1]=>3
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>[2,1,2,1,1]=>2
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)=>[3,3,1]=>3
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[4,2,1]=>4
([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[5,1,1]=>5
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>[6,1]=>6
([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>[1,6,1]=>1
([(0,8),(1,6),(2,6),(3,7),(4,5),(5,8),(6,7),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,7),(3,7),(4,8),(5,7),(5,8),(6,8)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,7),(1,7),(2,6),(3,6),(4,5),(5,8),(6,8),(7,8)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,1,2,1]=>2
([(0,1),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)=>[2,2,1,2,1,1]=>2
([(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(4,9),(5,6),(5,8),(6,7),(6,8),(7,9),(8,9)],10)=>[5,4,1]=>5
([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6)],8)=>[3,3,1,1]=>3
([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,3),(2,5),(2,7),(2,8),(3,4),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,8),(6,8),(7,8)],9)=>[1,3,3,1,1]=>1
([(0,2),(0,5),(0,7),(1,2),(1,4),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,3),(0,6),(0,7),(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(1,8),(2,3),(2,6),(2,8),(3,4),(3,5),(3,7),(3,8),(4,5),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,7),(0,8),(1,2),(1,3),(1,5),(1,6),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,8),(6,7),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,9),(3,5),(3,6),(3,9),(4,7),(4,8),(4,9),(5,6),(5,8),(5,9),(6,7),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,7),(0,8),(1,2),(1,3),(1,5),(1,6),(2,6),(2,8),(3,5),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[2,1,2,2,1,1]=>2
([(0,2),(0,5),(1,3),(1,4),(1,7),(2,4),(2,6),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,3),(1,6),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,7),(1,2),(1,6),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,8),(1,2),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,7),(1,8),(2,3),(2,6),(2,8),(3,4),(3,6),(4,7),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,5),(2,7),(2,8),(3,4),(3,6),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(0,8),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,9),(3,6),(3,7),(3,8),(3,9),(4,5),(4,7),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(0,8),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(3,8),(4,5),(4,7),(4,8),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(0,8),(1,2),(1,4),(1,6),(1,8),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,7),(1,9),(2,3),(2,5),(2,7),(2,8),(3,4),(3,5),(3,6),(3,8),(4,5),(4,6),(4,9),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,7),(1,2),(1,5),(1,7),(1,8),(2,3),(2,6),(2,8),(3,6),(3,8),(4,5),(4,6),(4,7),(5,6),(5,7),(5,8),(6,8),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,1),(0,5),(0,7),(0,8),(1,4),(1,7),(1,8),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,8),(4,6),(4,7),(5,6),(5,8),(6,7),(6,8),(7,8)],9)=>[2,2,2,2,1]=>2
([(0,3),(0,5),(0,7),(0,9),(1,2),(1,4),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,6),(3,7),(3,9),(4,5),(4,6),(4,8),(4,9),(5,6),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(0,8),(1,3),(1,4),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(3,6),(3,8),(4,5),(4,7),(5,8),(6,7)],9)=>[4,4,1]=>4
([(0,1),(0,2),(0,7),(0,8),(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(3,8),(3,9),(4,5),(4,7),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,2,2,1,2,1,1]=>1
([(0,1),(0,6),(0,7),(0,9),(1,4),(1,5),(1,8),(2,3),(2,5),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,9),(7,9),(8,9)],10)=>[1,2,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,7),(2,3),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,4),(0,5),(1,2),(1,3),(1,7),(1,8),(2,3),(2,6),(2,8),(3,6),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[2,1,1,2,1,1,1]=>2
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,8),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,6),(3,6),(3,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,5),(2,7),(2,8),(3,4),(3,7),(3,8),(4,5),(4,6),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)=>[1,2,1,1,2,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,6),(2,8),(3,5),(3,7),(3,8),(4,5),(4,6),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(1,4),(1,5),(1,6),(1,7),(2,6),(2,7),(2,8),(3,4),(3,5),(3,8),(4,5),(4,7),(4,8),(5,6),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,4),(0,5),(0,8),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,7),(2,9),(3,4),(3,6),(3,9),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)=>[3,1,3,1,1,1]=>3
([(0,1),(0,3),(0,4),(1,2),(1,4),(2,5),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,4),(0,8),(1,3),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,7),(4,6),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,8),(0,9),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,6),(3,8),(4,7),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[2,2,2,1,2,1]=>2
([(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,7),(4,8),(5,7),(6,8),(7,8)],9)=>[3,2,2,1,1]=>3
([(0,2),(0,5),(0,6),(0,8),(1,2),(1,3),(1,4),(1,7),(2,7),(2,8),(3,4),(3,5),(3,7),(3,9),(4,6),(4,8),(4,9),(5,6),(5,7),(5,9),(6,8),(6,9),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,6),(1,8),(1,9),(2,5),(2,7),(2,9),(3,4),(3,5),(3,7),(3,8),(4,6),(4,7),(4,8),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,8),(1,9),(2,3),(2,4),(2,6),(2,7),(2,9),(3,4),(3,5),(3,7),(3,8),(4,8),(4,9),(5,6),(5,7),(5,8),(6,7),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(0,8),(0,9),(1,2),(1,4),(1,6),(1,8),(2,4),(2,5),(2,7),(3,5),(3,6),(3,9),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[2,2,1,1,2,1,1]=>2
([(0,7),(0,8),(0,9),(1,2),(1,3),(1,5),(1,6),(1,9),(2,3),(2,4),(2,6),(2,8),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[2,2,1,1,2,1,1]=>2
([(0,1),(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,4,2]=>2
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[7,1]=>7
([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,2]=>6
([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,5,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,4,1,1]=>2
([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,1,2]=>1
([(0,7),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,2,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,3,1,1]=>3
([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,1,2]=>2
([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,2,1]=>2
([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,2,2]=>1
([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,3,1]=>1
([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,5]=>3
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,1,1]=>4
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,2]=>3
([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,2]=>1
([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,2,1]=>3
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,2,2]=>2
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,3,1]=>2
([(0,7),(1,7),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,4,1]=>1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,1,1,1]=>5
([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,1,1,2]=>4
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,1,1,1,1]=>2
([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,1,1]=>3
([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,2]=>2
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,2,1]=>2
([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,2]=>1
([(0,7),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,3,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,1,2,1]=>4
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,2,2]=>3
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,3]=>2
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,2,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,3,1]=>3
([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,3,2]=>2
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,4,1]=>2
([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,5,1]=>1
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[6,1,1]=>6
([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,1,2]=>5
([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,1,1,1]=>2
([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,2]=>1
([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,1,1]=>3
([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,1,1,2]=>2
([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,1,2,1]=>2
([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,2]=>1
([(0,7),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,3,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,1,1,1,1]=>4
([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,2]=>3
([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,3]=>2
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,2,1]=>3
([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,2]=>2
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,3,1]=>2
([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,2]=>1
([(0,7),(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,4,1]=>1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,2,1]=>5
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>4
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,2,1,1]=>1
([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,3]=>3
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,2,1,1]=>2
([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,2]=>1
([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,2,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,2,1,1]=>3
([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,2]=>2
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,3]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,2,1]=>2
([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,2]=>1
([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,3,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,3,1]=>4
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,3,2]=>3
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,3,1,1]=>1
([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,3]=>2
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,3,1,1]=>2
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,2]=>1
([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,2,1]=>1
([(3,7),(4,7),(5,7),(6,7)],8)=>[1,3,4]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,4,1]=>3
([(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)=>[1,1,4,1,1]=>1
([(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)=>[2,5,1]=>2
([],8)=>[8]=>8
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,2,2,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,4,1]=>2
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[1,3,3,1]=>1
([(0,7),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,2,1]=>1
([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,2,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,6),(0,7),(1,5),(1,7),(2,5),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,1,3,1]=>2
([(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,2,1,2,1]=>2
([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[2,2,3,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,3,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,3,1]=>3
([(0,5),(0,7),(1,4),(1,7),(2,3),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,1),(0,7),(1,7),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,2,1]=>2
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,2),(0,7),(1,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,3),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,3,1,1]=>2
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,3),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,4),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,2,1]=>3
([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,2,3,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,2),(0,3),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[2,1,2,2,1]=>2
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,4,1]=>3
([(0,2),(0,3),(0,4),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,1,1]=>2
([(0,4),(0,5),(0,7),(1,2),(1,3),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(0,5),(0,7),(1,2),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,1,1,1]=>2
([(0,1),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,3),(0,4),(0,5),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,1,1]=>3
([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,1,1]=>4
([(0,1),(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,1,1]=>3
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,1,1,1,1]=>4
([(0,3),(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,1,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,1,1]=>3
([(0,2),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,2,1,1,1]=>2
([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,1,1,1]=>2
([(0,1),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,2,1]=>3
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,2,1]=>5
([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[3,4,1]=>3
([(0,1),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,2,1]=>1
([(0,2),(0,3),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,2,1]=>1
([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(4,7),(5,6)],8)=>[2,6]=>2
([(4,7),(5,6),(6,7)],8)=>[1,1,1,5]=>1
([(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,5]=>1
([(2,7),(3,7),(4,6),(5,6)],8)=>[2,2,4]=>2
([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,3]=>1
([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,3]=>1
([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,1,2]=>1
([(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,4]=>1
([(1,5),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7)],8)=>[1,1,1,2,1,2]=>1
([(1,6),(2,3),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,2]=>1
([(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,2]=>1
([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,4,3]=>1
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,2,3,2]=>1
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,3,2]=>1
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,3,2]=>2
([(1,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[1,3,2,2]=>1
([(1,7),(2,6),(3,4),(3,5),(4,6),(5,7)],8)=>[1,1,1,1,1,1,2]=>1
([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8)=>[4,4]=>4
([(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,4]=>3
([(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,3]=>1
([(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,3]=>1
([(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,3,1,3]=>1
([(1,6),(1,7),(2,3),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,3,1,2]=>1
([(1,2),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(1,2),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,2]=>1
([(1,5),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,3]=>3
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,1,2]=>1
([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[2,3,3]=>2
([(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7)],8)=>[1,2,1,2,2]=>1
([(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,2]=>1
([(1,2),(1,6),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,2]=>2
([(1,5),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[2,4,2]=>2
([(1,2),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,3,2]=>2
([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,2,2]=>3
([(1,2),(1,3),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,3]=>3
([(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,2]=>1
([(1,2),(1,4),(1,7),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,2),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,2]=>3
([(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,1,1,2]=>2
([(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,2,2]=>2
([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>4
([(0,7),(1,6),(2,5),(3,4)],8)=>[4,4]=>4
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7)],8)=>[1,4,3]=>1
([(0,3),(1,2),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,3,3]=>2
([(0,1),(2,3),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,5),(0,7),(1,2),(1,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,2,1,2]=>2
([(0,1),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,4,1,2]=>1
([(0,1),(2,5),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)=>[1,2,2,1,2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,2]=>3
([(0,1),(0,7),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,2),(0,5),(0,6),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,6),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,7),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,7),(2,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,3),(1,6),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,3),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,4),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[2,2,3,1]=>2
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,3,1]=>1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,4,1]=>1
([(0,2),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,5,1]=>1
([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,4,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8)=>[1,6,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,4,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,4),(2,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,7),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,4),(1,7),(2,3),(2,4),(2,7),(3,6),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,4),(0,7),(1,2),(1,6),(2,5),(3,4),(3,5),(3,7),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(1,2),(1,3),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,3,2]=>3
([(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(5,6),(5,7)],8)=>[2,4,2]=>2
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8)=>[4,2,2]=>4
([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,3),(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)=>[1,2,4,1]=>1
([(2,7),(3,5),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,3]=>1
([(1,2),(1,7),(1,9),(2,6),(2,8),(3,4),(3,6),(3,8),(3,9),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,9),(7,8),(8,9)],10)=>[1,1,1,1,1,1,1,1,2]=>1
([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,3]=>3
([(0,1),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,2,2]=>2
([(0,1),(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,2]=>3
([(0,1),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,2]=>1
([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[5,1,2]=>5
([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,5),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[2,4,1,1]=>2
([(0,1),(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,2,1]=>1
([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,2),(0,3),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,4,1]=>1
([(0,1),(0,7),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,1),(0,5),(0,7),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,2),(0,3),(0,7),(1,2),(1,3),(1,7),(2,6),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,1),(0,5),(1,4),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(0,3),(1,2),(1,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>4
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8)=>[6,2]=>6
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,4,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,3),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)=>[1,4,2,1]=>1
([(0,10),(1,7),(2,7),(3,8),(4,9),(5,6),(6,10),(7,9),(8,9),(8,10)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,8),(1,7),(2,6),(3,6),(3,8),(4,7),(4,8),(5,6),(5,7),(5,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,8),(1,7),(2,5),(2,6),(3,7),(3,9),(4,8),(4,9),(5,7),(5,9),(6,8),(6,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,7),(1,3),(1,8),(2,7),(2,8),(3,5),(4,5),(4,6),(5,8),(6,7),(6,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(2,5),(3,4),(4,6),(5,7)],8)=>[1,2,2,2,1]=>1
([(0,8),(1,4),(1,8),(2,3),(2,6),(3,7),(4,5),(4,6),(5,7),(5,8),(6,7)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,9),(1,7),(1,8),(2,7),(2,11),(3,6),(3,8),(4,9),(4,11),(5,6),(5,9),(5,11),(6,10),(7,10),(8,10),(10,11)],12)=>[1,1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,8),(1,5),(1,7),(2,4),(2,6),(3,6),(3,7),(4,8),(4,9),(5,8),(5,9),(6,9),(7,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,4),(2,3),(3,8),(4,9),(5,7),(5,8),(6,7),(6,9),(7,10),(8,10),(9,10)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(1,2),(2,4),(3,5),(4,8),(5,9),(6,7),(6,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,10),(1,6),(1,10),(2,3),(2,8),(3,9),(4,5),(4,6),(4,8),(5,7),(5,9),(6,7),(7,10),(8,9)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,5),(2,7),(3,5),(3,6),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,9),(2,6),(3,7),(3,9),(4,6),(4,8),(5,7),(6,9),(7,8),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,9),(1,5),(2,9),(2,10),(3,7),(3,10),(4,6),(4,8),(5,7),(6,9),(6,10),(7,8),(8,10)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,9),(1,7),(1,8),(2,9),(2,10),(3,4),(3,5),(4,6),(5,6),(5,7),(6,10),(7,10),(8,9),(8,10)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,9),(1,3),(1,8),(2,8),(2,9),(3,5),(4,7),(4,9),(5,7),(5,8),(6,7),(6,8),(6,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(3,8),(4,7),(5,6),(6,8),(7,8)],9)=>[1,1,1,1,1,4]=>1
([(4,9),(5,8),(6,7),(7,9),(8,9)],10)=>[1,1,1,1,1,5]=>1
([(3,8),(4,7),(5,6),(5,7),(6,8),(7,8)],9)=>[1,1,1,1,1,4]=>1
([(3,6),(3,9),(4,5),(4,9),(5,8),(6,8),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,4]=>1
([(5,10),(6,9),(7,8),(8,10),(9,10)],11)=>[1,1,1,1,1,6]=>1
([(3,8),(4,6),(4,9),(5,7),(5,9),(6,7),(6,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,4]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[2,3,2,1]=>2
([(0,5),(0,6),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,4,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,3,1]=>1
([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,5),(1,5),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,6),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,4),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,2),(1,5),(1,7),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(2,3),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,1,1,1,2]=>3
([(0,7),(1,2),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)=>[4,1,1,2]=>4
([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(6,7)],8)=>[5,1,2]=>5
([(0,7),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],8)=>[4,2,2]=>4
([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(0,1),(0,2),(0,6),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,7),(1,4),(1,5),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,7),(5,6),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6)],8)=>[1,3,3,1]=>1
([(0,2),(0,3),(1,5),(1,6),(1,7),(2,4),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,2,2,1]=>1
([(0,7),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,6),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,3,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(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)=>[1,1,5,1]=>1
([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,1,1,1]=>1
([(0,7),(1,7),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,7),(1,7),(2,3),(2,6),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,5),(2,4),(3,6),(4,5),(6,7)],8)=>[2,2,2,2]=>2
([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8)=>[2,2,2,2]=>2
([(0,7),(1,6),(2,4),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8)=>[2,4,2]=>2
([(0,4),(0,5),(0,7),(1,2),(1,3),(1,6),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,2,1,1,1]=>1
([(0,2),(1,4),(1,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,7),(1,5),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,3),(1,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,2),(1,6),(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,7),(1,5),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,5),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,3),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,3),(1,7),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,3,2]=>1
([(0,6),(1,6),(2,7),(3,4),(3,5),(4,7),(5,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,7),(3,7),(4,6),(5,6),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(0,2),(0,6),(1,6),(1,7),(2,5),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,6),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(1,2),(1,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,6),(1,7),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,4),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(2,6),(3,4),(3,7),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,7),(1,3),(2,4),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(1,7),(2,6),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,6),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,1),(0,7),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6)],8)=>[1,3,3,1]=>1
([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,4),(2,6),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,7),(1,6),(2,3),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,7),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,7),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,1,1,1]=>1
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,4,2]=>1
([(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7)],8)=>[1,1,1,3,1,1]=>1
([(0,1),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,2]=>1
([(0,1),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,1,2]=>1
([(0,1),(2,7),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,4,2]=>1
([(0,7),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,5),(2,7),(3,4),(3,6),(4,7),(5,6)],8)=>[2,1,2,2,1]=>2
([(0,7),(0,8),(1,5),(1,6),(2,3),(2,4),(3,6),(3,8),(4,5),(4,7),(5,8),(6,7)],9)=>[1,2,1,2,2,1]=>1
([(0,7),(0,8),(0,9),(1,4),(1,6),(1,9),(2,3),(2,6),(2,8),(3,5),(3,9),(4,5),(4,8),(5,7),(6,7)],10)=>[4,5,1]=>4
([(0,7),(1,6),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,5),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,2,1,1,2,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(2,5),(2,7),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(2,3),(2,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(2,3),(2,6),(3,4),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,5),(1,6),(2,3),(2,4),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,8),(1,6),(1,7),(2,3),(2,4),(2,5),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,7),(2,3),(2,7),(3,6),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,8),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,8),(4,6),(5,6),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(0,8),(1,2),(1,5),(1,6),(2,7),(2,8),(3,5),(3,6),(4,5),(4,6),(4,7),(4,8),(5,8),(6,7)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,9),(1,4),(1,7),(1,8),(2,3),(2,5),(2,6),(3,7),(3,8),(4,5),(4,6),(5,8),(5,9),(6,7),(6,9),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(0,8),(1,5),(1,6),(2,6),(2,8),(3,5),(3,7),(4,5),(4,6),(4,7),(4,8),(5,8),(6,7)],9)=>[1,2,2,1,2,1]=>1
([(0,5),(0,7),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,7),(2,3),(2,6),(3,5),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(0,8),(1,6),(1,8),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,8),(5,8),(6,7),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,5),(0,7),(0,8),(1,4),(1,6),(1,8),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(4,7),(4,8),(5,6),(5,8)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(1,8),(2,3),(2,6),(2,7),(3,5),(3,8),(4,5),(4,7),(5,7),(5,8),(6,7),(6,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,8),(0,9),(1,5),(1,7),(1,9),(2,4),(2,7),(2,8),(3,4),(3,5),(3,7),(4,6),(4,9),(5,6),(5,8),(6,8),(6,9),(7,8),(7,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,8),(2,5),(2,7),(3,4),(3,6),(4,7),(4,8),(5,6),(5,8),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,8),(1,4),(1,7),(2,3),(2,6),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,8),(7,8)],9)=>[1,1,1,2,1,1,1,1]=>1
([(0,7),(0,8),(1,5),(1,6),(2,4),(2,6),(2,8),(3,4),(3,5),(3,7),(4,9),(5,8),(5,9),(6,7),(6,9),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(1,8),(2,3),(2,4),(2,6),(3,5),(3,8),(4,5),(4,7),(5,7),(5,8),(6,7),(6,8)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(3,7),(4,5),(4,8),(5,7),(5,8),(6,7),(6,8)],9)=>[2,2,2,2,1]=>2
([(0,7),(0,9),(1,6),(1,8),(2,3),(2,4),(2,5),(3,8),(3,9),(4,6),(4,7),(4,8),(5,6),(5,7),(5,9),(6,9),(7,8),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(0,9),(1,4),(1,5),(1,8),(2,5),(2,7),(2,8),(2,9),(3,4),(3,6),(3,8),(3,9),(4,7),(4,9),(5,6),(5,9),(6,8),(7,8)],10)=>[1,1,1,1,1,1,2,1,1]=>1
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,2,1]=>1
([(0,7),(0,8),(1,6),(1,8),(2,5),(2,8),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,8),(6,8),(7,8)],9)=>[1,1,2,1,1,2,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,5),(1,7),(1,8),(2,5),(2,6),(2,8),(3,4),(3,5),(3,6),(3,7),(4,5),(4,8),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(1,8),(2,3),(2,6),(2,8),(3,5),(3,8),(4,5),(4,8),(5,7),(6,7),(7,8)],9)=>[1,2,1,1,2,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(1,7),(2,3),(2,6),(2,8),(3,5),(3,7),(4,5),(4,8),(5,6),(5,8),(6,7),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,7),(0,8),(1,4),(1,6),(1,8),(2,3),(2,6),(2,8),(3,5),(3,8),(4,5),(4,8),(5,6),(5,7),(6,7),(7,8)],9)=>[1,1,1,1,2,1,1,1]=>1
([(0,8),(0,9),(1,6),(1,7),(1,9),(2,5),(2,7),(2,9),(3,5),(3,6),(3,8),(4,5),(4,6),(4,7),(4,8),(5,9),(6,9),(7,8),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,6),(1,7),(2,5),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(0,8),(1,5),(1,7),(1,8),(2,4),(2,5),(2,8),(3,4),(3,6),(3,7),(4,7),(4,8),(5,6),(5,7),(6,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(0,8),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,8),(4,5),(4,6),(4,8),(7,8)],9)=>[1,2,2,3,1]=>1
([(0,7),(0,8),(0,9),(1,2),(1,5),(1,6),(1,9),(2,3),(2,4),(2,8),(3,6),(3,7),(3,8),(4,5),(4,7),(4,9),(5,7),(5,8),(6,7),(6,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,9),(1,4),(1,8),(1,9),(2,3),(2,7),(2,9),(3,4),(3,5),(3,8),(4,6),(4,7),(5,7),(5,8),(6,7),(6,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(0,9),(1,4),(1,6),(1,9),(2,3),(2,8),(2,9),(3,4),(3,5),(3,9),(4,7),(4,8),(5,6),(5,8),(6,8),(6,9),(7,8),(7,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,3]=>1
([(0,1),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,1,1,2,2]=>2
([(0,1),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(0,7),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,1,2,2]=>1
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,1,1,1,1,2]=>2
([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,2]=>1
([(0,2),(0,3),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(0,1),(2,3),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,2]=>1
([(0,1),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,2]=>1
([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,2,2]=>1
([(0,5),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,4),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,2),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,5),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,5),(1,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,2),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,3),(1,5),(1,6),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,3),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7)],8)=>[1,3,2,2]=>1
([(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,2),(1,6),(1,7),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,3,1,1]=>1
([(0,5),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,5),(0,7),(1,5),(1,7),(2,3),(2,4),(2,7),(3,4),(3,6),(4,6),(5,6),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,7),(1,6),(2,6),(3,6),(4,5),(4,7),(5,7)],8)=>[2,1,3,2]=>2
([(0,5),(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(1,5),(1,7),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[3,2,1,2]=>3
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,2,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,3,2,1,1]=>1
([(0,1),(0,2),(0,6),(0,7),(1,2),(1,5),(1,7),(2,4),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(0,7),(1,3),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,7),(1,2),(1,4),(1,5),(1,6),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,1),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,4,2]=>2
([(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,2,3,1,1]=>1
([(0,3),(0,4),(0,5),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,4),(0,7),(1,3),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,4),(1,5),(1,6),(2,3),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,2,4,1]=>1
([(0,3),(1,2),(4,7),(5,6),(6,7)],8)=>[1,3,1,3]=>1
([(0,1),(2,7),(3,4),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,6),(1,7),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,4),(1,7),(2,6),(2,7),(3,5),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,7),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,5),(3,4),(4,6),(5,7),(6,7)],8)=>[1,1,2,1,1,2]=>1
([(0,3),(1,2),(3,6),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(0,1),(2,5),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,1),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(0,2),(1,5),(1,7),(2,6),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,7),(1,7),(2,3),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,6),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,6),(2,7),(3,5),(3,7),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,3),(2,7),(3,7),(4,5),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(1,7),(2,3),(2,7),(3,7),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,3),(1,7),(2,3),(2,7),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,2),(1,5),(1,7),(2,4),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(1,7),(2,6),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,4),(2,4),(2,7),(3,5),(3,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,7),(2,4),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,3),(1,7),(2,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(2,3),(2,7),(3,6),(4,5),(4,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,7),(2,4),(2,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,3),(2,7),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,3),(2,7),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(1,7),(2,5),(2,6),(3,4),(3,7),(4,7),(5,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(1,5),(2,7),(3,4),(3,7),(4,7),(5,6)],8)=>[1,1,1,1,1,1,2]=>1
([(0,7),(1,2),(1,7),(2,7),(3,4),(3,6),(4,6),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,2),(1,7),(2,7),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,4),(2,4),(3,5),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,7),(2,3),(2,5),(3,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,5),(2,6),(3,4),(3,7),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,7),(2,5),(2,6),(3,4),(3,5),(3,7),(4,6),(5,6),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,3),(2,6),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,3),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(1,2),(1,5),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(4,7),(5,7),(6,7)],8)=>[1,2,2,3]=>1
([(0,1),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,6),(0,7),(1,3),(1,5),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(2,3),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(0,1),(2,6),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,2]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,2,2,1]=>1
([(0,6),(1,2),(1,4),(1,7),(2,5),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,2,1]=>1
([(0,1),(0,2),(0,5),(0,6),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,6),(1,5),(1,7),(2,3),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(1,5),(1,7),(2,3),(2,4),(2,7),(3,5),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,2),(1,2),(1,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,4),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,2),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,3,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(1,2),(1,5),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,4,1]=>1
([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[2,1,2,1,1,1]=>2
([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,7),(1,5),(1,7),(2,4),(2,7),(3,4),(3,7),(4,6),(5,6),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,3),(1,7),(2,3),(2,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,5),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,6),(1,6),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,7),(2,3),(2,7),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,7),(2,7),(3,4),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,4),(1,4),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,7),(0,8),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,5),(2,6),(2,8),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,7),(0,8),(0,9),(1,2),(1,4),(1,5),(1,6),(1,8),(1,9),(2,3),(2,5),(2,6),(2,8),(2,9),(3,4),(3,5),(3,7),(3,8),(4,6),(4,7),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,2),(0,3),(0,4),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,4),(0,5),(0,6),(0,8),(1,2),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,7),(4,8),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,1),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(1,7),(2,5),(2,7),(3,6),(3,7),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,2),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,4),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,3),(0,5),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,7),(3,4),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,3),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,3,1,1]=>1
([(0,5),(0,7),(1,2),(1,3),(1,4),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,7),(1,4),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,7),(3,4),(3,5),(4,5),(6,7)],8)=>[1,2,1,1,1,2]=>1
([(0,7),(1,2),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,2),(1,4),(1,7),(2,4),(2,7),(3,4),(3,5),(3,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,3),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,3),(1,7),(2,5),(2,6),(2,7),(3,4),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,2,1,1,1]=>1
([(0,1),(0,5),(0,7),(1,4),(1,5),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,5,1,1]=>1
([(0,2),(0,7),(1,2),(1,5),(1,6),(1,7),(2,3),(2,4),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,1),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,2]=>1
([(0,3),(1,3),(1,7),(2,6),(2,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(1,3),(1,7),(2,4),(2,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,2,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,4),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,7),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,7),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,7),(1,2),(1,7),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,3),(0,6),(0,7),(0,8),(1,2),(1,4),(1,6),(1,7),(1,8),(2,4),(2,5),(2,7),(2,8),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[2,1,1,1,1,1,1,1]=>2
([(0,3),(0,8),(0,9),(1,2),(1,7),(1,9),(2,5),(2,7),(2,9),(3,6),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,9),(8,9)],10)=>[1,1,1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,7),(1,8),(2,3),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,8),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,2),(0,4),(0,5),(0,7),(0,8),(1,2),(1,3),(1,6),(1,7),(1,8),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,2,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,7),(0,8),(0,9),(0,10),(1,2),(1,4),(1,6),(1,7),(1,8),(1,9),(1,10),(2,3),(2,5),(2,6),(2,7),(2,9),(2,10),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10),(6,7),(6,8),(6,9),(6,10),(7,8),(7,9),(7,10),(8,9),(8,10),(9,10)],11)=>[1,1,1,1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,2,1,2,1,1]=>1
([(0,7),(1,2),(1,3),(1,5),(1,6),(2,4),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,5),(1,6),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,6),(2,6),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,4,1,2]=>1
([(0,6),(1,6),(2,5),(2,7),(3,4),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,6),(1,2),(1,7),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,5),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,4),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,2,3,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,2,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,1),(0,7),(1,7),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,3,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,2),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[4,2,2]=>4
([(0,1),(0,4),(1,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,3),(0,7),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,7),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,7),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,4,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,3,1,1]=>1
([(0,3),(1,2),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,3),(1,3),(1,6),(2,4),(2,5),(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(2,3),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,6),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(0,5),(1,4),(1,6),(1,7),(2,3),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,3),(1,7),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,1,1,1]=>1
([(0,1),(0,5),(0,6),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,7),(1,2),(1,4),(1,6),(2,3),(2,5),(2,7),(3,4),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,6),(2,3),(3,7),(4,5),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(1,6),(2,7),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,2),(1,4),(1,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(1,2),(1,4),(1,6),(1,7),(2,3),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,3),(1,7),(2,4),(2,6),(3,5),(3,6),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(1,7),(2,3),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,6),(1,7),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,5),(2,6),(2,7),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,6),(1,7),(2,4),(2,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,2,1,1,1]=>1
([(0,1),(0,7),(1,5),(1,6),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,3),(0,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(1,3),(1,4),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,3),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,6),(0,7),(1,4),(1,5),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(0,5),(0,7),(1,3),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,4),(0,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,4),(0,5),(1,3),(1,6),(1,7),(2,3),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,7),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,5),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,2),(1,5),(1,6),(2,4),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(2,3),(2,4),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)=>[1,2,3,1,1]=>1
([(0,6),(1,4),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,3,1,1,1]=>1
([(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
([(0,7),(1,3),(1,6),(2,4),(2,5),(2,7),(3,4),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,6),(2,7),(3,4),(3,5),(3,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,3),(0,7),(1,3),(1,4),(1,7),(2,4),(2,5),(2,7),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,4),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,4),(1,5),(2,3),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,4),(0,7),(1,3),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,5),(0,7),(1,5),(1,7),(2,4),(2,6),(3,4),(3,6),(4,7),(5,6),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,2,1]=>1
([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,2),(0,3),(0,6),(1,2),(1,5),(1,7),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,1),(0,2),(0,4),(0,7),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(1,7),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(0,7),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,6),(0,7),(1,3),(1,4),(1,5),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,4),(1,5),(2,3),(2,6),(2,7),(3,4),(3,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,5),(1,6),(1,7),(2,4),(2,6),(2,7),(3,4),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,1),(0,3),(0,4),(0,5),(0,7),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,4),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,2),(0,3),(0,4),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,3,1,1]=>1
([(2,5),(2,8),(3,4),(3,6),(3,8),(4,6),(4,7),(5,7),(5,8),(6,7),(6,8),(7,8)],9)=>[1,1,1,1,1,1,3]=>1
([(1,4),(1,9),(2,3),(2,8),(3,6),(3,8),(4,7),(4,9),(5,6),(5,7),(5,8),(5,9),(6,8),(6,9),(7,8),(7,9)],10)=>[1,1,1,1,1,1,1,1,2]=>1
([(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7)],9)=>[1,3,3,2]=>1
([(0,5),(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,3),(2,6),(2,7),(3,4),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(1,6),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,6),(2,3),(2,4),(3,4),(5,6),(5,7)],8)=>[1,2,1,1,1,2]=>1
([(0,4),(1,7),(2,5),(2,7),(3,5),(3,7),(4,6),(5,6),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,7),(1,5),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,3,1,1]=>1
([(0,7),(1,5),(1,6),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)=>[1,3,2,2]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,4,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,2,1,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,5),(1,7),(2,4),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,2),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[2,3,1,2]=>2
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(5,6),(5,7),(6,7)],8)=>[1,1,1,3,1,1]=>1
([(0,7),(1,5),(2,5),(2,7),(3,4),(3,6),(4,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,6),(1,6),(2,5),(2,7),(3,5),(3,7),(4,5),(4,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(3,4),(3,7),(4,7),(5,6),(5,7)],8)=>[1,3,1,1,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(4,5),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,2),(1,2),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[2,2,2,2]=>2
([(0,6),(1,6),(1,7),(2,5),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6)],8)=>[1,1,1,3,1,1]=>1
([(0,6),(1,2),(1,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,7),(5,7),(6,7)],8)=>[1,2,1,1,1,1,1]=>1
([(0,7),(1,5),(2,3),(2,6),(3,6),(4,6),(4,7),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,2),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,2),(1,5),(1,6),(1,7),(2,4),(2,5),(3,4),(3,5),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,7),(2,3),(2,6),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,2),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,4,1,1,1]=>1
([(0,1),(0,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,7),(1,6),(1,7),(2,3),(2,7),(3,5),(3,6),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,4),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(5,6),(5,7),(6,7)],8)=>[1,1,1,2,1,1,1]=>1
([(0,4),(0,5),(0,7),(1,2),(1,3),(1,4),(1,6),(2,3),(2,6),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,3),(1,6),(1,7),(2,3),(2,5),(2,6),(2,7),(3,4),(3,5),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,2),(1,4),(1,7),(2,5),(2,6),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,6),(1,5),(1,7),(2,3),(2,4),(2,5),(2,7),(3,4),(3,5),(3,7),(4,6),(4,7),(5,6),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,2),(1,7),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,2),(1,6),(1,7),(2,4),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(1,5),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,2,2,1,1]=>1
([(0,3),(0,4),(0,7),(1,2),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(4,5),(4,6),(5,7),(6,7)],8)=>[1,1,3,1,1,1]=>1
([(0,3),(0,6),(1,4),(1,6),(1,7),(2,4),(2,5),(2,7),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,4),(0,6),(0,7),(1,2),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,7),(4,5),(4,6),(4,7),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,7),(1,4),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,6),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,1),(0,2),(0,3),(0,5),(1,4),(1,6),(1,7),(2,4),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,2,1,1]=>1
([(0,1),(0,7),(1,4),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(3,7),(4,5),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,5),(1,2),(1,6),(1,7),(2,4),(2,5),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,1,1,1,1,1,1,1]=>1
([(0,3),(0,6),(0,7),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,2,1,2,1,1]=>1
([(0,2),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7)],8)=>[1,1,2,1,1,1,1]=>1
([(0,2),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>[1,3,1,1,1,1]=>1
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Description
The first part of an integer composition.
Map
Laplacian multiplicities
Description
The composition of multiplicities of the Laplacian eigenvalues.
Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices. Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.
Let $\lambda_1 > \lambda_2 > \dots$ be the eigenvalues of the Laplacian matrix of a graph on $n$ vertices. Then this map returns the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda_i$.
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