Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Images
[1] => [1,0] => [.,.] => ([],1)
[1,1] => [1,0,1,0] => [.,[.,.]] => ([(0,1)],2)
[2] => [1,1,0,0] => [[.,.],.] => ([(0,1)],2)
[1,1,1] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => ([(0,2),(1,2)],3)
[1,2] => [1,0,1,1,0,0] => [.,[[.,.],.]] => ([(0,2),(1,2)],3)
[2,1] => [1,1,0,0,1,0] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[3] => [1,1,1,0,0,0] => [[[.,.],.],.] => ([(0,2),(1,2)],3)
[1,1,1,1] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,2] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => ([(0,3),(1,2),(2,3)],4)
[1,2,1] => [1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(2,3)],4)
[1,3] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => ([(0,3),(1,2),(2,3)],4)
[2,1,1] => [1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[2,2] => [1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4)
[3,1] => [1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[4] => [1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,4] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[2,3] => [1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[3,2] => [1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[4,1] => [1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[5] => [1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
>>> Load all 360 entries. <<<
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[3,1,1,2,1] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[3,1,2,1,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[3,1,4] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[3,2,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[3,2,3] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[3,3,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[4,1,3] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[4,3,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[5,1,2] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[5,2,1] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,2,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,1,1,1,2,3] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,4,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,2,4] => [1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,5,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,2,5] => [1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,2,1,5] => [1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,7),(3,5),(4,6),(4,8),(5,6),(7,8)],9)
[1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,5,3] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,1,5] => [1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,1,6] => [1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,1,1,1,1,5] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,1,1,1,5,1] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,1,1,1,6] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,2,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,1,1,6,1] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,1,1,7] => [1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,2,1,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,2,1,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(3,7),(4,9),(5,8),(6,8),(7,9),(8,9)],10)
[1,2,7] => [1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,1,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,1,1,1,4] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,1,1,5] => [1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,1,7] => [1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,7),(1,9),(2,8),(3,5),(4,6),(5,8),(6,9),(7,8),(7,9)],10)
[2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[2,2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => ([(0,11),(1,10),(2,8),(3,9),(4,6),(5,7),(6,10),(7,11),(8,9),(8,10),(9,11)],12)
[1,2,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => ([(0,11),(1,10),(2,9),(3,7),(4,7),(5,8),(6,8),(7,10),(8,11),(9,10),(9,11)],12)
[1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.