Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ 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 364 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)
[1,1,1,1,2,3] => [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)
[1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[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)
[1,2,1,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],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)
[1,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,4,2,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.] => ([(0,8),(1,7),(2,6),(3,4),(4,7),(5,6),(5,8),(7,8)],9)
[1,5,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,6,1,1] => [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)
[2,1,1,1,2,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[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)
[2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[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)
[3,1,5] => [1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[3,2,1,1,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[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)
[4,1,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[4,1,4] => [1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[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)
[5,1,3] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[5,3,1] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[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)
[6,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[6,2,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(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)
[1,1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => ([(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)
[1,1,1,1,6] => [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)
[1,1,1,7] => [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)
[1,2,1,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,3,1,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,5,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,6,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,7,2] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(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)
[2,1,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[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)
[4,5,1] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[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)
[7,2,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[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)
[1,1,1,1,1,1,1,1,1,2] => [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: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.