Identifier
-
Mp00251:
Graphs
—clique sizes⟶
Integer partitions
Mp00322: Integer partitions —Loehr-Warrington⟶ Integer partitions
St000378: Integer partitions ⟶ ℤ
Values
([],1) => [1] => [1] => 1
([],2) => [1,1] => [2] => 2
([(0,1)],2) => [2] => [1,1] => 1
([],3) => [1,1,1] => [2,1] => 3
([(1,2)],3) => [2,1] => [3] => 2
([(0,2),(1,2)],3) => [2,2] => [4] => 2
([(0,1),(0,2),(1,2)],3) => [3] => [1,1,1] => 1
([],4) => [1,1,1,1] => [3,1] => 4
([(2,3)],4) => [2,1,1] => [2,2] => 3
([(1,3),(2,3)],4) => [2,2,1] => [2,2,1] => 3
([(0,3),(1,3),(2,3)],4) => [2,2,2] => [2,2,2] => 3
([(0,3),(1,2)],4) => [2,2] => [4] => 2
([(0,3),(1,2),(2,3)],4) => [2,2,2] => [2,2,2] => 3
([(1,2),(1,3),(2,3)],4) => [3,1] => [2,1,1] => 2
([(0,3),(1,2),(1,3),(2,3)],4) => [3,2] => [5] => 2
([(0,2),(0,3),(1,2),(1,3)],4) => [2,2,2,2] => [5,1,1,1] => 4
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [3,3] => [6] => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => [1,1,1,1] => 1
([],5) => [1,1,1,1,1] => [3,2] => 5
([(3,4)],5) => [2,1,1,1] => [3,1,1] => 4
([(2,4),(3,4)],5) => [2,2,1,1] => [4,1,1] => 4
([(1,4),(2,4),(3,4)],5) => [2,2,2,1] => [4,1,1,1] => 4
([(0,4),(1,4),(2,4),(3,4)],5) => [2,2,2,2] => [5,1,1,1] => 4
([(1,4),(2,3)],5) => [2,2,1] => [2,2,1] => 3
([(1,4),(2,3),(3,4)],5) => [2,2,2,1] => [4,1,1,1] => 4
([(0,1),(2,4),(3,4)],5) => [2,2,2] => [2,2,2] => 3
([(2,3),(2,4),(3,4)],5) => [3,1,1] => [4,1] => 3
([(0,4),(1,4),(2,3),(3,4)],5) => [2,2,2,2] => [5,1,1,1] => 4
([(1,4),(2,3),(2,4),(3,4)],5) => [3,2,1] => [5,1] => 3
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [3,2,2] => [2,2,2,1] => 3
([(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,1] => [5,4] => 5
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => [2,2,2,2,2] => [6,4] => 5
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,1] => [6,1] => 3
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2] => [2,2,2,1] => 3
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,2] => [2,2,2,2] => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => [2,2,2,2,1] => 3
([(0,4),(1,3),(2,3),(2,4)],5) => [2,2,2,2] => [5,1,1,1] => 4
([(0,1),(2,3),(2,4),(3,4)],5) => [3,2] => [5] => 2
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => [3,2,2] => [2,2,2,1] => 3
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => [3,3] => [6] => 2
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) => [2,2,2,2,2] => [6,4] => 5
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) => [3,3,3] => [2,2,2,2,1] => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => [3,3,2] => [2,2,2,2] => 3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => [2,1,1,1] => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,2] => [2,2,1,1] => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,3] => [7] => 2
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,4] => [8] => 2
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => [1,1,1,1,1] => 1
([],6) => [1,1,1,1,1,1] => [3,2,1] => 6
([(4,5)],6) => [2,1,1,1,1] => [4,2] => 5
([(3,5),(4,5)],6) => [2,2,1,1,1] => [4,3] => 5
([(2,5),(3,5),(4,5)],6) => [2,2,2,1,1] => [5,3] => 5
([(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,1] => [5,4] => 5
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(2,5),(3,4)],6) => [2,2,1,1] => [4,1,1] => 4
([(2,5),(3,4),(4,5)],6) => [2,2,2,1,1] => [5,3] => 5
([(1,2),(3,5),(4,5)],6) => [2,2,2,1] => [4,1,1,1] => 4
([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => [3,3] => 4
([(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,1] => [5,4] => 5
([(0,1),(2,5),(3,5),(4,5)],6) => [2,2,2,2] => [5,1,1,1] => 4
([(2,5),(3,4),(3,5),(4,5)],6) => [3,2,1,1] => [5,2] => 4
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => [3,2,2,1] => 4
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,1,1] => [3,3,3,1] => 6
([(0,5),(1,5),(2,4),(3,4)],6) => [2,2,2,2] => [5,1,1,1] => 4
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,1,1] => [6,2] => 4
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,1] => [3,2,2,1] => 4
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => [3,2,2,2] => 4
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [3,2,2,2,1] => 4
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,5),(1,4),(2,3)],6) => [2,2,2] => [2,2,2] => 3
([(1,5),(2,4),(3,4),(3,5)],6) => [2,2,2,2,1] => [5,4] => 5
([(0,1),(2,5),(3,4),(4,5)],6) => [2,2,2,2] => [5,1,1,1] => 4
([(1,2),(3,4),(3,5),(4,5)],6) => [3,2,1] => [5,1] => 3
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,1] => [3,2,2,1] => 4
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2] => [2,2,2,1] => 3
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,1] => [6,1] => 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,2] => [2,2,2,2] => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,1] => [3,2,2,2] => 4
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
>>> Load all 816 entries. <<<([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,1] => [3,2,2,2,1] => 4
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2] => [6,4] => 5
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) => [3,2,2] => [2,2,2,1] => 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => [2,2,2,2] => 3
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => [3,2,2,2,2] => [6,5] => 5
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2] => [2,2,2,2] => 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3] => [2,2,2,2,1] => 3
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => [3,1,1,1] => 3
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,1] => [5,1,1] => 3
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [6,1,1] => 3
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,1] => [7,1] => 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [6,1,1] => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [7,1,1] => 3
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [2,2,2,2,2] => 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3,2] => [8,6] => 5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [6,5] => 5
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => [3,2,2,2,2] => [6,5] => 5
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => [7,6] => 5
([(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] => [8,7] => 5
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3,2] => [8,6] => 5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,1] => [8,1] => 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [7,1,1] => 3
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [8,1,1] => 3
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2] => [7,6] => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [2,2,2,2,2] => 3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,3] => [2,2,2,2,2,1] => 3
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [2,2,2,2,2,2] => 3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) => [3,3] => [6] => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) => [3,3,2] => [2,2,2,2] => 3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2] => [2,2,1,1] => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => [3,3,3] => [2,2,2,2,1] => 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2] => [6,1,1] => 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3] => [7] => 2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,2] => [7,1,1] => 3
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [3,3,3,3] => [7,1,1,1,1,1] => 4
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,2,2,2] => [5,5] => 4
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [2,2,2,2,2] => 3
([(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] => [7,1,1,1,1,1] => 4
([(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] => [8] => 2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => [3,3,2,2,2] => [7,5] => 5
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => [3,3,3,2,2] => [7,6] => 5
([(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] => [8,7] => 5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) => [3,3,2,2,2] => [7,5] => 5
([(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] => [8,6] => 5
([(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] => [8,7] => 5
([(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] => [2,2,2,2,2,2] => 3
([(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] => [3,3,2,2,1] => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,3,3] => [2,2,2,2,2] => 3
([(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] => [2,2,2,2,2,1] => 3
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,4,2] => [8,1,1] => 3
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => [2,1,1,1,1] => 2
([(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] => [2,2,1,1,1] => 2
([(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] => [2,2,2,1,1] => 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) => [5,4] => [9] => 2
([(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] => [8,4] => 4
([(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] => [3,3,2,2,2] => 4
([(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] => [10] => 2
([(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] => [1,1,1,1,1,1] => 1
([],7) => [1,1,1,1,1,1,1] => [4,2,1] => 7
([(5,6)],7) => [2,1,1,1,1,1] => [3,3,1] => 6
([(4,6),(5,6)],7) => [2,2,1,1,1,1] => [3,3,2] => 6
([(3,6),(4,6),(5,6)],7) => [2,2,2,1,1,1] => [3,3,2,1] => 6
([(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1,1] => [3,3,3,1] => 6
([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(3,6),(4,5)],7) => [2,2,1,1,1] => [4,3] => 5
([(3,6),(4,5),(5,6)],7) => [2,2,2,1,1,1] => [3,3,2,1] => 6
([(2,3),(4,6),(5,6)],7) => [2,2,2,1,1] => [5,3] => 5
([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => [3,2,2] => 5
([(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1,1] => [3,3,3,1] => 6
([(1,2),(3,6),(4,6),(5,6)],7) => [2,2,2,2,1] => [5,4] => 5
([(3,6),(4,5),(4,6),(5,6)],7) => [3,2,1,1,1] => [3,3,1,1] => 5
([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,1),(2,6),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2] => [6,4] => 5
([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => [3,3,3] => 5
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,1,1,1] => [5,2,2,2] => 7
([(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,1] => [5,4] => 5
([(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,1,1] => [5,2,2,2,1] => 7
([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => [2,2,2,2,2] => [6,4] => 5
([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,1,1,1] => [5,2,1,1] => 5
([(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,1,1] => [3,3,3] => 5
([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [6,2,2] => 5
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,1,1] => [6,5,1,1,1] => 8
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => 8
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [4,2,2,2,1] => 5
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,2] => [8,6] => 5
([(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] => [8,7] => 5
([(1,6),(2,5),(3,4)],7) => [2,2,2,1] => [4,1,1,1] => 4
([(2,6),(3,5),(4,5),(4,6)],7) => [2,2,2,2,1,1] => [3,3,3,1] => 6
([(1,2),(3,6),(4,5),(5,6)],7) => [2,2,2,2,1] => [5,4] => 5
([(0,3),(1,2),(4,6),(5,6)],7) => [2,2,2,2] => [5,1,1,1] => 4
([(2,3),(4,5),(4,6),(5,6)],7) => [3,2,1,1] => [5,2] => 4
([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,1),(2,6),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2] => [6,4] => 5
([(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,1,1] => [3,3,3] => 5
([(1,2),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,1] => [3,2,2,1] => 4
([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,1,1] => [6,2] => 4
([(0,6),(1,6),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,1] => [3,2,2,2] => 4
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,1,1] => [5,2,2,2,1] => 7
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1,1] => [6,4,1] => 6
([(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,1,1] => [6,2,2] => 5
([(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [6,5,1] => 6
([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,6),(1,6),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1,1] => [4,2,2,2,1] => 5
([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(1,6),(2,5),(3,4),(3,5),(4,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(1,2),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,1] => [3,3,3,2] => 6
([(0,6),(1,5),(2,4),(3,4),(5,6)],7) => [2,2,2,2,2] => [6,4] => 5
([(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,1] => [3,2,2,1] => 4
([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => [3,2,2,2] => 4
([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,1),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,1] => [5,2,1,1,1] => 5
([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [6,5,1] => 6
([(0,5),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,6),(1,5),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,1] => [3,2,2,2] => 4
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [3,2,2,2,1] => 4
([(0,6),(1,5),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => [3,2,1,1] => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1,1] => [4,4] => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [6,3] => 4
([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => 8
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(0,6),(1,5),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,5),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [8,6] => 5
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,5),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(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] => [7,1,1,1,1,1] => 4
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,6),(2,3),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1,1] => [7,2] => 4
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [6,3] => 4
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [7,3] => 4
([(0,6),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(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] => [3,3,2,2,1] => 4
([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(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] => [8,6] => 5
([(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] => [8,6] => 5
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,7] => 5
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2,1] => [4,3,3,3,2] => 7
([(0,6),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [3,2,2,2,2] => 4
([(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] => [3,3,2,2,1] => 4
([(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] => [3,3,2,2,2] => 4
([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => 8
([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1,1] => [7,3,1,1] => 6
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2,2,1] => [6,5,1,1,1,1] => 8
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [6,5,1] => 6
([(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,1] => [6,5,1] => 6
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [3,2,2,2,2,1] => [6,5,1] => 6
([(0,4),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,2),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,2),(1,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,2),(1,6),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(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] => [8,6] => 5
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,4),(1,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,4),(1,4),(1,6),(2,5),(2,6),(3,5),(3,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(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] => [7,1,1,1,1,1] => 4
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2,1] => [4,3,3,3,2] => 7
([(0,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,5),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,4),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,4),(0,6),(1,4),(1,6),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,1),(0,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,3),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,6] => 5
([(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] => [8,6] => 5
([(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] => [7,6] => 5
([(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] => [8,7] => 5
([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,1,1] => [8,2] => 4
([(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] => [8,3] => 4
([(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] => [3,3,2,2,1] => 4
([(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] => [8,4] => 4
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,5),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [7,3] => 4
([(0,6),(1,5),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(0,6),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,1] => [3,2,2,2,2] => 4
([(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] => [3,3,2,2,1] => 4
([(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] => [8,6] => 5
([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,3,2] => [3,3,2,2,2] => 4
([(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,6),(1,5),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(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] => [8,6] => 5
([(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] => [8,7] => 5
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [3,2,2,2,2,1] => 4
([(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] => [8,4] => 4
([(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] => [3,3,2,2,2,1] => 4
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,2,2,2] => 4
([(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] => [8,7] => 5
([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2,1] => [4,3,3,3,2,1] => 7
([(0,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,4),(1,5),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,4),(0,5),(1,4),(1,5),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 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) => [4,4,4,1] => [3,2,2,2,2,2] => 4
([(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] => [3,3,2,2,2,1] => 4
([(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] => [3,3,2,2,2,2] => 4
([(0,1),(2,5),(3,4),(4,6),(5,6)],7) => [2,2,2,2,2] => [6,4] => 5
([(0,3),(1,2),(4,5),(4,6),(5,6)],7) => [3,2,2] => [2,2,2,1] => 3
([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,1),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2] => [2,2,2,2] => 3
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3] => [2,2,2,2,1] => 3
([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [2,2,2,2,2,2] => [3,3,3,2,1] => 6
([(0,6),(1,5),(2,3),(2,4),(3,4),(5,6)],7) => [3,2,2,2] => [5,1,1,1,1] => 4
([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,1),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,2),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,6),(1,4),(2,3),(2,5),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,5),(1,4),(2,3),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,4),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,5),(1,4),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,4),(1,3),(2,5),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,4),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,3),(1,5),(1,6),(2,4),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(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] => [7,1,1,1,1,1] => 4
([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) => [3,3,1] => [6,1] => 3
([(1,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,1),(2,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,1] => [3,2,2,2] => 4
([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) => [3,3,2] => [2,2,2,2] => 3
([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,1] => [5,1,1] => 3
([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,1] => [3,2,2,2,1] => 4
([(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,1] => [6,3] => 4
([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => [6,1,1] => 3
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,6),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,1] => [7,1] => 3
([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [7,1,1] => 3
([(0,5),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,5),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(0,6),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,4),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,5),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,3),(1,5),(1,6),(2,4),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,4),(1,2),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,3),(0,6),(1,2),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,4),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [8,6] => 5
([(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] => [8,6] => 5
([(0,1),(0,6),(1,5),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,7] => 5
([(0,6),(1,5),(2,3),(2,4),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(1,5),(1,6),(2,3),(2,4),(3,4),(3,6),(4,5),(5,6)],7) => [3,3,2,2,1] => [6,2,1,1,1] => 5
([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,3),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,1] => [6,2,1,1,1,1] => 5
([(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2,1] => [7,3] => 4
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2,1] => [3,3,3,1,1] => 5
([(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] => [7,6] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [8,6] => 5
([(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] => [3,2,2,2,2] => 4
([(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] => [3,3,3,3] => 5
([(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] => [3,3,2,2,2] => 4
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [7,1,1] => 3
([(0,6),(1,2),(1,5),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3] => [2,2,2,2,1] => 3
([(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] => [7,6] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [7,1,1,1,1,1] => 4
([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3,2] => [7,1,1] => 3
([(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] => [2,2,2,2,2] => 3
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [7,6] => 5
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [3,3,2,2,2] => 4
([(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] => [8,7] => 5
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,3,2,2] => 5
([(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] => [8,6] => 5
([(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] => [8,1] => 3
([(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] => [8,1,1] => 3
([(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] => [2,2,2,2,2,1] => 3
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(4,6)],7) => [2,2,2,2,2,2,2] => [6,2,2,2,2] => 7
([(0,3),(1,4),(1,5),(2,4),(2,6),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,1),(0,3),(1,2),(2,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,2),(1,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,3),(1,2),(1,5),(2,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,6),(1,2),(1,6),(2,4),(3,4),(3,5),(4,5),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,1),(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,1),(0,2),(1,6),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,3),(0,6),(1,2),(1,6),(2,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,5),(1,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,5),(1,3),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2] => [7,6] => 5
([(0,1),(0,6),(1,3),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [7,6] => 5
([(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] => [8,6] => 5
([(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] => [8,7] => 5
([(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,2),(1,5),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,3,2,2,2,1] => [7,5,1] => 6
([(0,6),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [3,3,3,2,2] => 5
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,5),(0,6),(1,2),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,5),(1,2),(1,4),(1,6),(2,3),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2,1] => [8,3] => 4
([(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] => [3,3,2,2,1] => 4
([(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] => [3,2,2,2,2] => 4
([(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] => [6,2,2,1,1] => 5
([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [8,4] => 4
([(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,3,1] => [3,2,2,2,2,1] => 4
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,3,2,2] => 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) => [4,4,3,2] => [3,3,2,2,2,1] => 4
([(0,5),(0,6),(1,4),(1,5),(2,3),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [3,3,2,2,2] => 4
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [3,3,2,2,2,1] => 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) => [4,4,3,2] => [3,3,2,2,2,1] => 4
([(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] => [3,2,2,2,2,2] => 4
([(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] => [3,3,2,2,2,2] => 4
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,6),(4,6),(5,6)],7) => [3,2,2,2,2,2] => [3,3,3,3,1] => 6
([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,2),(1,4),(1,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,1),(0,6),(1,6),(2,3),(2,5),(3,4),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,3,2] => [8,6] => 5
([(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] => [7,6] => 5
([(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] => [8,7] => 5
([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,1),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,3),(0,5),(1,4),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,4),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,1),(0,6),(1,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,4),(1,2),(1,3),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,3),(0,4),(1,2),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,4),(0,6),(1,3),(1,5),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [7,6] => 5
([(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] => [7,6] => 5
([(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] => [7,6] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [3,3,3,3] => 5
([(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] => [8,6] => 5
([(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] => [3,3,3,2,2] => 5
([(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] => [8,7] => 5
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,2,2,1] => 4
([(0,5),(0,6),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [7,6] => 5
([(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] => [6,1,1,1,1,1] => 4
([(0,5),(0,6),(1,2),(1,5),(2,3),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,4),(1,3),(1,6),(2,3),(2,5),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,6] => 5
([(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] => [7,6] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [8,6] => 5
([(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] => [8,6] => 5
([(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] => [3,3,3,3] => 5
([(0,1),(0,5),(1,4),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,6] => 5
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,2,2,2] => 4
([(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] => [8,7] => 5
([(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] => [3,3,3,2,2] => 5
([(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] => [7,6] => 5
([(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] => [7,1,1,1,1,1] => 4
([(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] => [3,3,2,2,1] => 4
([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,4,2] => [8,1,1] => 3
([(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] => [7,1,1,1,1,1] => 4
([(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] => [8,7] => 5
([(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] => [8,4] => 4
([(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] => [2,2,2,2,2] => 3
([(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] => [2,2,2,2,2,1] => 3
([(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] => [7,6] => 5
([(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] => [7,6] => 5
([(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] => [3,3,3,3] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [8,6] => 5
([(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] => [8,7] => 5
([(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] => [3,3,2,2,2] => 4
([(0,4),(0,6),(1,2),(1,3),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [3,3,2,2,2,1] => 4
([(0,4),(0,6),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,7] => 5
([(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] => [8,1,1] => 3
([(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] => [2,2,2,2,2,1] => 3
([(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] => [2,2,2,2,2,2] => 3
([(0,5),(0,6),(1,2),(1,3),(2,3),(4,5),(4,6)],7) => [3,2,2,2,2] => [6,5] => 5
([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2] => [6,1,1] => 3
([(0,6),(1,2),(1,4),(2,4),(3,5),(3,6),(4,5),(5,6)],7) => [3,3,2,2] => [6,1,1,1,1] => 4
([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3] => [2,2,2,2,1] => 3
([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,2,2,2] => [7,5] => 5
([(0,1),(0,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(0,1),(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,2,2,2] => [5,5] => 4
([(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] => [3,3,3,3] => 5
([(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] => [7,1,1,1,1,1] => 4
([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => [7,1,1] => 3
([(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] => [2,2,2,2,2] => 3
([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => [3,1,1,1,1] => 3
([(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] => [8,4] => 4
([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,2,1] => [4,1,1,1,1] => 3
([(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] => [6,1,1,1] => 3
([(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] => [3,3,2,2,2,1] => 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) => [5,3,1] => [3,2,2,1,1] => 3
([(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] => [6,1,1,1] => 3
([(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] => [7,1,1,1] => 3
([(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] => [8,1,1,1] => 3
([(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] => [3,3,2,2,2,2] => 4
([(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] => [3,3,2,2,2,2] => 4
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [3,3,3,2,2] => 5
([(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] => [8,6] => 5
([(0,5),(0,6),(1,2),(1,3),(1,4),(2,3),(2,6),(3,5),(4,5),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,6] => 5
([(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] => [3,3,3,2,2] => 5
([(0,4),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [8,6] => 5
([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [4,4,2,2,1] => [6,2,2,1,1,1] => 5
([(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] => [3,3,3,2,2] => 5
([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [7,1,1,1,1,1] => 4
([(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] => [8,4] => 4
([(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] => [3,3,2,2,2,1] => 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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [9,1] => 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) => [5,3,2] => [7,1,1,1] => 3
([(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] => [9,1,1] => 3
([(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] => [8,1,1,1] => 3
([(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] => [9,1,1,1] => 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),(4,5),(4,6),(5,6)],7) => [5,4,4] => [2,2,2,2,2,2,1] => 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),(5,6)],7) => [4,4,3,3,3] => [9,8] => 5
([(0,2),(0,6),(1,2),(1,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,4),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5)],7) => [3,2,2,2,2,2,2] => [6,2,2,2,2,1] => 7
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(0,4),(0,5),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(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] => [7,6] => 5
([(0,3),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(0,5),(0,6),(1,2),(1,4),(1,6),(2,3),(2,6),(3,4),(3,5),(4,5)],7) => [3,3,2,2,2,2] => [3,3,3,3,2] => 6
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,6),(3,6),(4,6),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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] => [8,6] => 5
([(0,4),(0,6),(1,2),(1,3),(1,6),(2,5),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => [3,3,3,2,2,2] => [3,3,3,3,2,1] => 6
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [3,3,2,2,2,2] => 4
([(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] => [8,7] => 5
([(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] => [8,4] => 4
([(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] => [8,7] => 5
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [10,1] => 3
([(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] => [9,1,1] => 3
([(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] => [10,1,1] => 3
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [8,1,1,1] => 3
([(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] => [9,1,1,1] => 3
([(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] => [2,2,2,2,2,2,1] => 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) => [5,5,4] => [2,2,2,2,2,2,2] => 3
([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => [3,3,3,2] => [6,1,1,1,1,1] => 4
([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,3] => [7] => 2
([(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] => [7,1,1,1,1,1] => 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => [4,3,2] => [7,1,1] => 3
([(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] => [2,2,2,2,2] => 3
([(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] => [8] => 2
([(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] => [3,3,3,2,2] => 5
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,3,2,2] => 5
([(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] => [3,3,2,2,2] => 4
([(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] => [3,3,2,2,2,1] => 4
([(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] => [7,6] => 5
([(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] => [8,6] => 5
([(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] => [3,3,2,2,1] => 4
([(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] => [8,6] => 5
([(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] => [8,7] => 5
([(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] => [2,2,2,2,2] => 3
([(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] => [3,3,2,2,2] => 4
([(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] => [2,2,2,2,2,1] => 3
([(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] => [8,4] => 4
([(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] => [2,2,1,1,1] => 2
([(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] => [2,2,2,2,2,1] => 3
([(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] => [6,1,1,1] => 3
([(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] => [2,2,2,1,1] => 2
([(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] => [2,2,2,2,2,1] => 3
([(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] => [2,2,2,2,2,2] => 3
([(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] => [3,3,2,2,2,1] => 4
([(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] => [7,1,1,1] => 3
([(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] => [7,4] => 4
([(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] => [8,1,1,1] => 3
([(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] => [9] => 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)],7) => [4,3,3,2] => [3,3,2,2,2] => 4
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [3,3,3,2,2] => 5
([(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) => [3,3,3,3,3,2] => [3,3,3,3,3,2] => 6
([(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] => [8,7] => 5
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [3,3,2,2,2,1] => 4
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [9,1,1] => 3
([(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] => [6,6] => 4
([(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] => [9,1,1,1] => 3
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [3,3,3,2,2,1] => 4
([(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] => [2,2,2,2,2,2,1] => 3
([(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] => [10] => 2
([(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) => [4,4,3,3,3] => [9,8] => 5
([(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] => [8,5] => 4
([(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] => [3,3,3,2,2,2] => 4
([(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] => [2,2,2,2,2,2,1] => 3
([(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] => [2,2,2,2,2,2,2] => 3
([(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] => [9,1,1,1] => 3
([(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] => [10,1,1] => 3
([(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] => [2,1,1,1,1,1] => 2
([(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] => [2,2,1,1,1,1] => 2
([(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] => [2,2,2,1,1,1] => 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) => [6,4] => [2,2,2,2,1,1] => 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),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,5] => [11] => 2
([(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] => [9,5] => 4
([(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) => [5,5,3,3] => [10,6] => 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) => [6,6] => [12] => 2
([(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] => [1,1,1,1,1,1,1] => 1
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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 1,2,1 1,4,4,2 1,6,12,10,4,1
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = q + 2\ q^{2} + q^{3}$
$F_{4} = q + 4\ q^{2} + 4\ q^{3} + 2\ q^{4}$
$F_{5} = q + 6\ q^{2} + 12\ q^{3} + 10\ q^{4} + 4\ q^{5} + q^{6}$
Description
The diagonal inversion number of an integer partition.
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
The dinv of a partition is the number of cells $c$ in the diagram of an integer partition $\lambda$ for which $\operatorname{arm}(c)-\operatorname{leg}(c) \in \{0,1\}$.
See also exercise 3.19 of [2].
This statistic is equidistributed with the length of the partition, see [3].
Map
clique sizes
Description
The integer partition of the sizes of the maximal cliques of a graph.
Map
Loehr-Warrington
Description
Return a partition whose diagonal inversion number is the length of the preimage.
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