Identifier
-
Mp00251:
Graphs
—clique sizes⟶
Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000659: Dyck paths ⟶ ℤ
Values
([],2) => [1,1] => [1,1,0,0] => 1
([(0,1)],2) => [2] => [1,0,1,0] => 0
([],3) => [1,1,1] => [1,1,0,1,0,0] => 1
([(1,2)],3) => [2,1] => [1,0,1,1,0,0] => 1
([(0,2),(1,2)],3) => [2,2] => [1,1,1,0,0,0] => 1
([(0,1),(0,2),(1,2)],3) => [3] => [1,0,1,0,1,0] => 0
([],4) => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 1
([(2,3)],4) => [2,1,1] => [1,0,1,1,0,1,0,0] => 1
([(1,3),(2,3)],4) => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
([(0,3),(1,3),(2,3)],4) => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
([(0,3),(1,2)],4) => [2,2] => [1,1,1,0,0,0] => 1
([(0,3),(1,2),(2,3)],4) => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
([(1,2),(1,3),(2,3)],4) => [3,1] => [1,0,1,0,1,1,0,0] => 1
([(0,3),(1,2),(1,3),(2,3)],4) => [3,2] => [1,0,1,1,1,0,0,0] => 1
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,0,1,0,1,0,1,0] => 0
([],5) => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 1
([(3,4)],5) => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 1
([(2,4),(3,4)],5) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
([(1,4),(2,4),(3,4)],5) => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
([(0,4),(1,4),(2,4),(3,4)],5) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(1,4),(2,3)],5) => [2,2,1] => [1,1,1,0,0,1,0,0] => 1
([(1,4),(2,3),(3,4)],5) => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
([(0,1),(2,4),(3,4)],5) => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
([(2,3),(2,4),(3,4)],5) => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 1
([(0,4),(1,4),(2,3),(3,4)],5) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(1,4),(2,3),(2,4),(3,4)],5) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(1,3),(2,3),(2,4)],5) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(0,1),(2,3),(2,4),(3,4)],5) => [3,2] => [1,0,1,1,1,0,0,0] => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 1
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
([],6) => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => 1
([(4,5)],6) => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
([(3,5),(4,5)],6) => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
([(2,5),(3,5),(4,5)],6) => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(2,5),(3,4)],6) => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 1
([(2,5),(3,4),(4,5)],6) => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(1,2),(3,5),(4,5)],6) => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
([(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,1),(2,5),(3,5),(4,5)],6) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(2,5),(3,4),(3,5),(4,5)],6) => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,4),(2,3)],6) => [2,2,2] => [1,1,1,1,0,0,0,0] => 1
([(1,5),(2,4),(3,4),(3,5)],6) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,1),(2,5),(3,4),(4,5)],6) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(1,2),(3,4),(3,5),(4,5)],6) => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 1
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
>>> Load all 750 entries. <<<([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 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) => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [1,1,1,0,1,0,0,0] => 1
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 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) => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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) => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
([],7) => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
([(5,6)],7) => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
([(4,6),(5,6)],7) => [2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1
([(3,6),(4,6),(5,6)],7) => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
([(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(3,6),(4,5)],7) => [2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => 1
([(3,6),(4,5),(5,6)],7) => [2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
([(2,3),(4,6),(5,6)],7) => [2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
([(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
([(1,2),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(3,6),(4,5),(4,6),(5,6)],7) => [3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(1,6),(2,5),(3,4)],7) => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 1
([(2,6),(3,5),(4,5),(4,6)],7) => [2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
([(1,2),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,3),(1,2),(4,6),(5,6)],7) => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 1
([(2,3),(4,5),(4,6),(5,6)],7) => [3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 1
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 2
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
([(0,6),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 1
([(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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 1
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 2
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,5),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 2
([(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,6),(1,3),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => 1
([(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) => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,6),(1,3),(1,6),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,6),(1,3),(1,5),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(1,2),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
([(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 2
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 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),(5,6)],7) => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,1),(0,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,3),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,3),(0,6),(1,3),(1,5),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,4),(1,6),(2,3),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,1),(0,5),(1,5),(2,3),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,1),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(1,4),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,4),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 1
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 1
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 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) => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 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) => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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) => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(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) => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,3),(1,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,4),(0,5),(1,3),(1,6),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(1,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 1
([(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,6),(1,2),(1,5),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 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) => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(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) => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 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) => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 1
([(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) => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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) => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 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),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 1
([(0,1),(0,6),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 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) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
([(0,3),(0,6),(1,2),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 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) => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 2
([(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) => [5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 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) => [5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => 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) => [4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
([(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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 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) => [4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 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) => [4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
([(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) => [4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 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) => [5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 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) => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
([(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) => [4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 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),(4,6),(5,6)],7) => [4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => 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) => [4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 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) => [5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 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) => [5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 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) => [5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 2
([(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) => [5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 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) => [5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 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) => [5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
([(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) => [5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 2
([(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) => [5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 2
([(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] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
([(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) => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 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) => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 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) => [5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 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) => [5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 2
([(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) => [6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 1
([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,3 1,10 1,30,3
$F_{2} = 1 + q$
$F_{3} = 1 + 3\ q$
$F_{4} = 1 + 10\ q$
$F_{5} = 1 + 30\ q + 3\ q^{2}$
Description
The number of rises of length at least 2 of a Dyck path.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
clique sizes
Description
The integer partition of the sizes of the maximal cliques of a graph.
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