Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
St000010: Integer partitions ⟶ ℤ
Values
[1,0] => [1] => ([],1) => [1] => 1
[1,0,1,0] => [1,1] => ([(0,1)],2) => [2] => 1
[1,1,0,0] => [2] => ([],2) => [1,1] => 2
[1,0,1,0,1,0] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => [3] => 1
[1,0,1,1,0,0] => [1,2] => ([(1,2)],3) => [2,1] => 2
[1,1,0,0,1,0] => [2,1] => ([(0,2),(1,2)],3) => [3] => 1
[1,1,0,1,0,0] => [3] => ([],3) => [1,1,1] => 3
[1,1,1,0,0,0] => [3] => ([],3) => [1,1,1] => 3
[1,0,1,0,1,0,1,0] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => 1
[1,0,1,0,1,1,0,0] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => [3,1] => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => [4] => 1
[1,0,1,1,0,1,0,0] => [1,3] => ([(2,3)],4) => [2,1,1] => 3
[1,0,1,1,1,0,0,0] => [1,3] => ([(2,3)],4) => [2,1,1] => 3
[1,1,0,0,1,0,1,0] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => [4] => 1
[1,1,0,0,1,1,0,0] => [2,2] => ([(1,3),(2,3)],4) => [3,1] => 2
[1,1,0,1,0,0,1,0] => [3,1] => ([(0,3),(1,3),(2,3)],4) => [4] => 1
[1,1,0,1,0,1,0,0] => [4] => ([],4) => [1,1,1,1] => 4
[1,1,0,1,1,0,0,0] => [4] => ([],4) => [1,1,1,1] => 4
[1,1,1,0,0,0,1,0] => [3,1] => ([(0,3),(1,3),(2,3)],4) => [4] => 1
[1,1,1,0,0,1,0,0] => [4] => ([],4) => [1,1,1,1] => 4
[1,1,1,0,1,0,0,0] => [4] => ([],4) => [1,1,1,1] => 4
[1,1,1,1,0,0,0,0] => [4] => ([],4) => [1,1,1,1] => 4
[1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => 2
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => [3,1,1] => 3
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => [3,1,1] => 3
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,0,1,1,0,0,1,1,0,0] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => 2
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,0,1,1,0,1,0,1,0,0] => [1,4] => ([(3,4)],5) => [2,1,1,1] => 4
[1,0,1,1,0,1,1,0,0,0] => [1,4] => ([(3,4)],5) => [2,1,1,1] => 4
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,0,1,1,1,0,0,1,0,0] => [1,4] => ([(3,4)],5) => [2,1,1,1] => 4
[1,0,1,1,1,0,1,0,0,0] => [1,4] => ([(3,4)],5) => [2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,4] => ([(3,4)],5) => [2,1,1,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [4,1] => 2
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,1,0,0,1,1,0,1,0,0] => [2,3] => ([(2,4),(3,4)],5) => [3,1,1] => 3
[1,1,0,0,1,1,1,0,0,0] => [2,3] => ([(2,4),(3,4)],5) => [3,1,1] => 3
[1,1,0,1,0,0,1,0,1,0] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,1,0,1,0,0,1,1,0,0] => [3,2] => ([(1,4),(2,4),(3,4)],5) => [4,1] => 2
[1,1,0,1,0,1,0,0,1,0] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5] => 1
[1,1,0,1,0,1,0,1,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,0,1,0,1,1,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,0,1,1,0,0,0,1,0] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5] => 1
[1,1,0,1,1,0,0,1,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,0,1,1,0,1,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,0,1,1,1,0,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,0,0,0,1,0,1,0] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => [5] => 1
[1,1,1,0,0,0,1,1,0,0] => [3,2] => ([(1,4),(2,4),(3,4)],5) => [4,1] => 2
[1,1,1,0,0,1,0,0,1,0] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5] => 1
[1,1,1,0,0,1,0,1,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,0,0,1,1,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,0,1,0,0,0,1,0] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5] => 1
[1,1,1,0,1,0,0,1,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,0,1,0,1,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,0,1,1,0,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,1,0,0,0,0,1,0] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => [5] => 1
[1,1,1,1,0,0,0,1,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,1,0,0,1,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,1,0,1,0,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,1,1,1,1,0,0,0,0,0] => [5] => ([],5) => [1,1,1,1,1] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1] => ([(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
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => ([(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
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,2,1,1,1] => ([(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) => [6] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
>>> Load all 1324 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,5] => ([(4,5)],6) => [2,1,1,1,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1] => ([(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
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4] => ([(3,5),(4,5)],6) => [3,1,1,1] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,1,1] => ([(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) => [6] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => [3,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,1,1] => ([(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) => [6] => 1
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [5,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3] => ([(2,5),(3,5),(4,5)],6) => [4,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => [6] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => [5,1] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,1,0,0,0,1,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => [6] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => [6] => ([],6) => [1,1,1,1,1,1] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1] => ([(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
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => ([(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] => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => ([(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) => [7] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => ([(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
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => ([(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
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => ([(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
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => ([(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) => [7] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => ([(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) => [7] => 1
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => ([(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) => [6,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => ([(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) => [7] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1] => ([(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) => [7] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => ([(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) => [6,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,2,2,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,6] => ([(5,6)],7) => [2,1,1,1,1,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,1,1,1,1] => ([(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
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5] => ([(4,6),(5,6)],7) => [3,1,1,1,1] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => ([(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) => [6,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => ([(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) => [6,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,2,2] => ([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4] => ([(3,6),(4,6),(5,6)],7) => [4,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => [5,1,1] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [6,1] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => [7] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7] => ([],7) => [1,1,1,1,1,1,1] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,1,2,1,1] => ([(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => ([(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,1,2,1,2] => ([(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => ([(1,7),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => ([(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [4,1,1,1,1] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,2,2,2] => ([(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => ([(2,7),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,2,1,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [1,2,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => ([(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,4,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => ([(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => ([(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => ([(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => ([(0,7),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => ([(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => ([(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => ([(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => ([(1,7),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,2,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => ([(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => ([(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,2,2,2] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => ([(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => ([(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,3] => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => ([(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => ([(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => ([(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => ([(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => ([(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => ([(0,7),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [3,2,1,1,1] => ([(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => ([(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => ([(0,7),(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,1,1,1,1] => ([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => ([(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => ([(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [6,1,1] => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => ([(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [4,2,2] => ([(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [7,1] => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => ([(0,7),(1,7),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4] => ([(3,7),(4,7),(5,7),(6,7)],8) => [5,1,1,1] => 4
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,1,1,1] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => [8] => 1
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8] => ([],8) => [1,1,1,1,1,1,1,1] => 8
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searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,1,2 5,2,2,5 14,5,4,5,14 42,14,10,10,14,42 132,42,28,25,28,42,132
$F_{1} = q$
$F_{2} = q + q^{2}$
$F_{3} = 2\ q + q^{2} + 2\ q^{3}$
$F_{4} = 5\ q + 2\ q^{2} + 2\ q^{3} + 5\ q^{4}$
$F_{5} = 14\ q + 5\ q^{2} + 4\ q^{3} + 5\ q^{4} + 14\ q^{5}$
$F_{6} = 42\ q + 14\ q^{2} + 10\ q^{3} + 10\ q^{4} + 14\ q^{5} + 42\ q^{6}$
$F_{7} = 132\ q + 42\ q^{2} + 28\ q^{3} + 25\ q^{4} + 28\ q^{5} + 42\ q^{6} + 132\ q^{7}$
Description
The length of the partition.
Map
touch composition
Description
Sends a Dyck path to its touch composition given by the composition of lengths of its touch points.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
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