Identifier
-
Mp00100:
Dyck paths
—touch composition⟶
Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001060: Graphs ⟶ ℤ
Values
[1,0,1,0,1,1,0,0] => [1,1,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0] => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,1,0,0] => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,0] => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0] => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,0] => [1,1,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0,1,0] => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,0] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,0] => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,0] => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0] => [2,2,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,2] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,1,1,2,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,3] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,2,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,2,2] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,2,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,1] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,2,1,2,1] => [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) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
>>> Load all 1563 entries. <<<[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [2,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,1,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [3,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [3,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [3,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,3,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [4,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [4,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,3] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,1,1,2,2] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,1,1,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,1,1,3,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,1,2,2,1] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,2,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,2,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,1,3,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,3,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,4,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,5] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,2,1,1,2] => [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) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,2,1,2,1] => [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) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,2,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,2,1,3] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,2,2,1,1] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,2,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,3,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,3,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,4,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,2,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,2,1,1,2,1] => [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) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [1,2,1,2,1,1] => [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) => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,2,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,3,1] => [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) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,2,1,3,1] => [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) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [1,2,2,1,2] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,2,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,2,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [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) => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [1,3,1,1,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [1,3,1,2,1] => [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) => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,3,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,3,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,3,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [1,4,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [1,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,1,1,2,1] => [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) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,1,2,1,1] => [1,2,1,2] => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,2,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,1,2,1,2] => [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) => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,3,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,2,1,1,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,2,1,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,2,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,2,1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,1,1] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [3,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [3,2,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,3,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,3,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [3,3,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [4,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [4,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [4,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [5,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [5,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,6] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,1,1,2,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,3,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,2,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,3,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,1,2,1,1,3] => [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) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [1,1,2,1,2,2] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,2,2,2,1] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,1,2,2,3] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [1,1,2,3,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,1,2,4,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,1,2,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,1,3,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [1,2,2,1,1,2] => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [1,2,2,2,1,1] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,2,2,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,3,1,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [1,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [1,4,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,1,1,1,2,2] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,1,1,3,1] => [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) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,1,2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,1,4,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,3,3] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,2,1,1,1,2] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,2,1,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [2,2,2,1,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,2,2,2,1] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,2,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,2,3,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [2,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [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) => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,2,1,2] => [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) => 3
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [4,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => [4,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => [4,3,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,5,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [1,1,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [1,1,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [1,2,1,3,1,2] => [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) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,2,2,2,2,1] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,2,3,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,2,3,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [1,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,1,1,5] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,1,4,1,2] => [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) => 3
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,2,1,1,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,2,2,2,1,1] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,2,3,3] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,3,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [2,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [2,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [3,3,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [5,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0] => [6,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0] => [7,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,1,1,1,1,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,1,1,1,1,2] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [1,1,2,1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,1,1,3,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,2,2,2,1] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,1,1,2,1] => [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) => 2
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,1,1,1,4] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [1,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,1,0,0] => [5,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [1,4,1,1,1,2] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [5,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,1,3,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,1,3,4] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,1,1,3,1] => [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) => 2
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,1,1,3,1] => [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) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [4,1,1,2,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [2,2,2,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,2,3,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,2,2,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,1,0,0] => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [2,5,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,2,4,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,5,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,4,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,1,6,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,7,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [1,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,5,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,1,1,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [4,1,1,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [4,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [4,1,1,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [5,1,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [4,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,5,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,1,6,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,4,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,4,1,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,2,2,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,1,0,0] => [5,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,1,1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [1,1,2,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,2,4] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,1,1,2,3] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [1,2,4,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [1,1,4,1,2] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,5] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,1,1,1,5] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,4,2] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,5,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [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) => 2
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,3,1,3,1] => [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) => 3
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [1,1,2,1,3,1] => [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) => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [1,3,1,1,2,1] => [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) => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,1,4,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,2,4,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,2,2,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,2,2,2,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,2,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,9,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [4,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [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) => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,1,4,1] => [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) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [1,5,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,4,1,3,1] => [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) => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,6,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0] => [1,5,1,2,1] => [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) => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,2,1,6] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0,1,1,0,0] => [1,8,1,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,4,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,2,5,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,2,5] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,1,1,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0,1,0] => [6,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [1,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,1,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,2,2] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,2] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,2,2,2,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,2,2,4,2] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,2,6] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,2,4,2,2] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,2,4,4] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,2,6,2] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,4,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,4,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [2,6,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [2,6,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [4,2,2,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [4,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,4,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,5,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [1,7,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [1,3,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [1,5,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,4,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,2,4,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [1,1,5,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,1,3,1,1,2] => [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) => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,3] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,2,6] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,2,6] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [4,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [1,7,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [6,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [6,5,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,6] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,1,1,6] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,9] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,2,2,4] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [4,4,1] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [4,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [5,2,2,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,1,1,1,4] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,6,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,4,2,2] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,4,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,2,2,1] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [3,1,1,4] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [1,8,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,1,1,1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [3,4,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [4,4,1,1] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,1,5,2] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [4,1,4,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,0,1,0] => [6,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0,1,0] => [7,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,1,0,1,0,0] => [6,1,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,1,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,1,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,2,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,4,4,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [3,1,2,1,5] => [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) => 3
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,1,3,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,3,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,3,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,1,1,0,0,1,0] => [9,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [6,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,1,6,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [1,6,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [5,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [2,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,2,6] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [4,3,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [3,5,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,3,4] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,1,3,1] => [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) => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [3,1,1,3,1] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,1,7] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,3,5] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [1,1,8] => [2,1] => ([(0,2),(1,2)],3) => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [1,1,1,7] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,4] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [3,1,6] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [3,1,2,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [5,1,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,7,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,3,1] => [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) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,3,3,1] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [5,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [1,6,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,5,2,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [1,1,5,5] => [2,2] => ([(1,3),(2,3)],4) => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,2,2,2,4] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,1,3,5] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [1,10,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [1,1,6,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,5,2,3,1] => [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) => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,2,3,1] => [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) => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,8,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [3,5,3,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,3,2,3,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [5,6,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [5,3,3,1] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [5,4,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,5,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,5,1] => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,1,1,6,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,2,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [1,7,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [5,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [1,1,2,1,1,3] => [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) => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,5,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,5,4] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [1,4,1,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,4,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,1,1,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,1,4] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,1,4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,1,1,1,4] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [5,1,2,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,5] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,2,2,2,3] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,2,2,2,5] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,2,2,4,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [1,2,4,2,3] => [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) => 3
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [1,2,9] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,4,2,2,3] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,4,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,4,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [1,6,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [1,8,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,2,2,2,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,2,4,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [3,2,7] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,2,3] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [3,6,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [5,2,2,3] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [5,2,5] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [5,4,3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 3
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Description
The distinguishing index of a graph.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
This is the smallest number of colours such that there is a colouring of the edges which is not preserved by any automorphism.
If the graph has a connected component which is a single edge, or at least two isolated vertices, this statistic is undefined.
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
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
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