Identifier
Mp00034:
Dyck paths
—to binary tree: up step, left tree, down step, right tree⟶
Binary trees
Mp00013: Binary trees —to poset⟶ Posets
Mp00013: Binary trees —to poset⟶ Posets
Images
[1,0] => [.,.] => ([],1)
[1,0,1,0] => [.,[.,.]] => ([(0,1)],2)
[1,1,0,0] => [[.,.],.] => ([(0,1)],2)
[1,0,1,0,1,0] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3)
[1,0,1,1,0,0] => [.,[[.,.],.]] => ([(0,2),(2,1)],3)
[1,1,0,0,1,0] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[1,1,0,1,0,0] => [[.,[.,.]],.] => ([(0,2),(2,1)],3)
[1,1,1,0,0,0] => [[[.,.],.],.] => ([(0,2),(2,1)],3)
[1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,1,0,0,1,0] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4)
[1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4)
[1,1,0,0,1,0,1,0] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,1,0,0] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4)
[1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4)
[1,1,1,0,0,0,1,0] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],.] => ([(0,3),(1,3),(3,2)],4)
[1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4)
[1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,1,0,1,1,0,0,0] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,1,1,1,0,0,1,0,0,0] => [[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,1,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
>>> Load all 2681 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[.,.]],.],.]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[.,.]],.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[.,.]]]],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,.]]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[.,.]]],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,0,1,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[.,.]],.]],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,0,1,1,1,0,1,0,0,0,0] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,1,1,1,1,0,0,0,0,0] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],.]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],.]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[.,.]]],.] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,[.,.]],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[[.,.],.],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,1,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[.,.]]],.],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,1,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,1,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,1,0,0,0,0,0,1,0] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,1,1,1,1,0,0,0,1,0,0,0] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[[.,.],[.,.]],.],.]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[[[.,.],[.,.]],.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[[[.,.],[.,.]],.]],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,.]],[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,.],[[.,.],[.,.]]],.]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,.]]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[[.,.],[[.,.],.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[[[[[.,.],.],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,.]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[[[.,.],[.,.]],.]]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,.],[[.,.],[.,.]]]],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,.],[.,.]]],.]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[[[.,.],.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[[[[.,.],[.,.]],.],.]],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[[.,.],[.,.]]]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[[[.,.],[.,.]],.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[[.,.],[.,.]]]],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[[.,.],[.,[.,.]]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],[[.,.],.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,[[[.,.],.],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,.],.],[[.,.],[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,.]],.],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],.]],.] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,.],[[.,.],[.,.]]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,.],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,.]],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[[.,.],[.,.]]],.],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[.,.],.],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[[[.,.],.],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[[[[.,.],[[.,.],.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[.,.],[.,.]],.],.],.],.] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,.],.]],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[.,[[.,.],[[.,[.,.]],.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[.,[[.,[.,.]],[[.,.],.]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[.,[[.,[[.,.],.]],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[.,[[[.,.],[.,.]],[.,.]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [.,[.,[.,[[[.,.],[[.,.],.]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[.,[[[.,[.,.]],.],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[.,[[[[.,.],[.,.]],.],.]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,.],[.,[[.,[.,.]],.]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[.,[[.,.],[[.,[.,.]],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [.,[.,[[.,.],[[[.,.],[.,.]],.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,[.,.]],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,[.,.]],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [.,[.,[[.,[.,.]],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[.,[[.,[.,[.,.]]],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [.,[.,[[.,[.,[.,[[.,.],.]]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [.,[.,[[.,[.,[[.,.],.]]],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [.,[.,[[.,[.,[[.,.],[.,.]]]],.]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [.,[.,[[.,[.,[[.,[.,.]],.]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [.,[.,[[.,[.,[[[.,.],.],.]]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[.,[[.,[[.,.],.]],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[.,[[.,[[.,.],[.,.]]],[.,.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[.,[[.,[[.,.],[.,[.,.]]]],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [.,[.,[[.,[[.,.],[[.,.],.]]],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[.,[[.,[[.,[.,.]],.]],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[.,[[.,[[.,[.,.]],[.,.]]],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[.,[[.,[[.,[.,[.,.]]],.]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,[[.,.],.]],.]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[.,[[.,[[[.,.],.],.]],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[.,[[.,[[[.,.],.],[.,.]]],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[.,[[.,[[[.,.],[.,.]],.]],.]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,[[[[.,.],.],.],.]],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[.,[[[.,.],[.,.]],[.,[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[.,[[[.,.],[.,.]],[[.,.],.]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[.,[[[.,.],[.,[.,.]]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [.,[.,[[[.,.],[.,[[.,.],.]]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [.,[.,[[[.,.],[[.,.],.]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[[.,.],[.,.]]],.]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [.,[.,[[[.,.],[[.,[.,.]],.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [.,[.,[[[.,.],[[[.,.],.],.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[.,[[[.,[.,.]],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[.,[[[.,[.,.]],.],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[.,[[[.,[.,.]],[.,.]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [.,[.,[[[.,[.,.]],[[.,.],.]],.]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[.,[[[.,[.,[.,.]]],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[.,[[[.,[[.,.],.]],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[[.,.],[.,.]]],.],.]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[.,[[[[.,.],.],[.,.]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [.,[.,[[[[.,.],.],[[.,.],.]],.]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[.,[[[[.,.],[.,.]],.],[.,.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[.,[[[[.,.],[.,.]],[.,.]],.]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],[.,[.,.]]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],[[.,.],.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[.,[[[[.,[.,.]],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[.,[[[[.,[.,.]],[.,.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [.,[.,[[[[.,[[.,.],.]],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [.,[.,[[[[[.,.],.],[.,.]],.],.]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[[.,[.,.]],.]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [.,[[.,.],[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [.,[[.,.],[.,[[.,[.,[.,.]]],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [.,[[.,.],[.,[[.,[[.,.],.]],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [.,[[.,.],[.,[[[.,.],[.,.]],.]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [.,[[.,.],[.,[[[.,[.,.]],.],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,[.,.]],.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [.,[[.,.],[[.,[.,.]],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [.,[[.,.],[[.,[.,.]],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,[.,.]]],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,.],[[.,[.,[.,[.,.]]]],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [.,[[.,.],[[.,[.,[[.,.],.]]],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [.,[[.,.],[[.,[[.,.],.]],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [.,[[.,.],[[.,[[.,.],[.,.]]],.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [.,[[.,.],[[.,[[.,[.,.]],.]],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [.,[[.,.],[[.,[[[.,.],.],.]],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [.,[[.,.],[[[.,.],[.,.]],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [.,[[.,.],[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [.,[[.,.],[[[.,[.,.]],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [.,[[.,.],[[[.,[.,[.,.]]],.],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [.,[[.,.],[[[.,[[.,.],.]],.],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [.,[[.,.],[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [.,[[.,.],[[[[.,.],[.,.]],.],.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [.,[[.,.],[[[[.,[.,.]],.],.],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,.]],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [.,[[.,[.,.]],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,.]],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[.,.]],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,.]],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [.,[[.,[.,.]],[[.,[[.,.],.]],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [.,[[.,[.,.]],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [.,[[.,[.,.]],[[[.,[.,.]],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [.,[[.,[.,.]],[[[[.,.],.],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[.,.]]],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [.,[[.,[.,[.,.]]],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [.,[[.,[.,[.,.]]],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [.,[[.,[.,[.,.]]],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,[.,.]]]],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [.,[[.,[.,[.,[[.,.],.]]]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [.,[[.,[.,[[.,.],.]]],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [.,[[.,[.,[[.,.],.]]],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [.,[[.,[.,[[.,.],[.,.]]]],[.,.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [.,[[.,[.,[[.,.],[.,[.,.]]]]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [.,[[.,[.,[[.,.],[[.,.],.]]]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [.,[[.,[.,[[.,[.,.]],.]]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],[.,.]]]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [.,[[.,[.,[[[.,.],.],.]]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],[.,.]]]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [.,[[.,[.,[[[.,.],[.,.]],.]]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [.,[[.,[[.,.],.]],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [.,[[.,[[.,.],.]],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [.,[[.,[[.,.],.]],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [.,[[.,[[.,.],.]],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [.,[[.,[[.,.],[.,.]]],[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [.,[[.,[[.,.],[.,.]]],[[.,.],.]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [.,[[.,[[.,.],[.,[.,.]]]],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [.,[[.,[[.,.],[[.,.],.]]],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],[.,.]]]],.]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [.,[[.,[[.,[.,.]],.]],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [.,[[.,[[.,[.,.]],.]],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [.,[[.,[[.,[.,.]],[.,.]]],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [.,[[.,[[.,[.,.]],[.,[.,.]]]],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [.,[[.,[[.,[.,.]],[[.,.],.]]],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[.,[.,[.,.]]],[.,.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[[.,[.,[[.,.],.]]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [.,[[.,[[.,[[.,.],.]],.]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,[[.,.],.]],[.,.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[[.,.],[.,.]]],.]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,.],.],.]],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [.,[[.,[[[.,.],.],.]],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [.,[[.,[[[.,.],.],.]],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [.,[[.,[[[.,.],.],[.,.]]],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [.,[[.,[[[.,.],[.,.]],.]],[.,.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],[.,.]],[.,.]]],.]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[.,[[[.,.],[[.,.],.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [.,[[.,[[[.,[.,.]],.],.]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[.,.]],.],[.,.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [.,[[.,[[[.,[.,.]],[.,.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,[.,.]]],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [.,[[.,[[[.,[[.,.],.]],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[[.,[[[[.,.],.],.],.]],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [.,[[.,[[[[.,.],.],[.,.]],.]],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [.,[[.,[[[[.,.],[.,.]],.],.]],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[[.,[.,.]],.],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [.,[[[.,.],.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [.,[[[.,.],.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [.,[[[.,.],.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [.,[[[.,.],.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],.],[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [.,[[[.,.],.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [.,[[[.,.],[.,.]],[.,[[.,.],.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,5),(3,5),(5,7),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [.,[[[.,.],[.,.]],[[.,[.,.]],.]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [.,[[[.,.],[.,.]],[[[.,.],.],.]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [.,[[[.,.],[.,[.,.]]],[.,[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [.,[[[.,.],[.,[.,.]]],[[.,.],.]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [.,[[[.,.],[.,[.,[.,.]]]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [.,[[[.,.],[.,[.,[[.,.],.]]]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [.,[[[.,.],[.,[[.,.],.]]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [.,[[[.,.],[.,[[.,.],[.,.]]]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [.,[[[.,.],[.,[[.,[.,.]],.]]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],.],.]]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],[[.,.],.]],[.,[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],[[.,.],.]],[[.,.],.]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[[.,.],[.,.]]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[[.,.],[.,[.,.]]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [.,[[[.,.],[[.,.],[[.,.],.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [.,[[[.,.],[[.,[.,.]],.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,.],[[.,[.,.]],[.,.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,.],[[.,[.,[.,.]]],.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,.],[[.,[[.,.],.]],.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],[[[.,.],.],.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],[[[.,.],.],[.,.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [.,[[[.,.],[[[.,.],[.,.]],.]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [.,[[[.,.],[[[.,[.,.]],.],.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [.,[[[.,[.,.]],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [.,[[[.,[.,.]],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [.,[[[.,[.,.]],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [.,[[[.,[.,.]],[.,.]],[[.,.],.]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [.,[[[.,[.,.]],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [.,[[[.,[.,.]],[[.,.],.]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [.,[[[.,[.,.]],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [.,[[[.,[.,[.,.]]],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [.,[[[.,[.,[.,.]]],[.,.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [.,[[[.,[.,[.,.]]],[[.,.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,.]]]],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [.,[[[.,[.,[[.,.],.]]],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [.,[[[.,[.,[[.,.],[.,.]]]],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [.,[[[.,[[.,.],.]],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [.,[[[.,[[.,.],.]],[.,.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [.,[[[.,[[.,.],.]],[[.,.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[.,.],[.,.]]],.],[.,.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],[.,.]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[.,.]],.]],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],[.,.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [.,[[[.,[[.,[[.,.],.]],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [.,[[[.,[[[.,.],.],.]],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[[.,.],.],.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [.,[[[[.,.],.],[.,.]],[.,[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [.,[[[[.,.],.],[.,.]],[[.,.],.]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [.,[[[[.,.],.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [.,[[[[.,.],.],[[.,.],.]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [.,[[[[.,.],[.,.]],.],[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [.,[[[[.,.],[.,.]],.],[[.,.],.]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[.,.],[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [.,[[[[.,.],[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [.,[[[[.,.],[[.,.],.]],.],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [.,[[[[.,[.,.]],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [.,[[[[.,[.,.]],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[.,.]],.],[.,.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [.,[[[[.,[.,.]],.],[[.,.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [.,[[[[.,[.,.]],[.,.]],.],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,[.,.]]],.],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [.,[[[[.,[.,.]],[[.,.],.]],.],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,[.,.]]],[.,.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [.,[[[[.,[[.,.],.]],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [.,[[[[.,[[.,.],.]],[.,.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[[.,[[.,[.,.]],.]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [.,[[[[[.,.],.],.],[.,.]],[.,.]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [.,[[[[[.,.],.],[.,.]],.],[.,.]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[[[.,.],[.,.]],.],.],[.,.]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [.,[[[[[.,[.,.]],.],[.,.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[.,.]],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[.,[.,.]],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[.,.]],[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[.,.]],[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[.,.]],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[.,[.,.]],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0] => [[.,[.,.]],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[.,.]],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[.,.]],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[.,.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[.,[.,.]],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[.,.]],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[.,.]],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[.,.]],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[.,.]],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[.,[.,.]],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,.]]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[.,[.,[.,.]]],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,[.,[.,.]]],[[.,[.,.]],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,[[.,.],.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [[.,[.,[.,.]]],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [[.,[.,[.,.]]],[[[.,[.,.]],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,.]]]]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[.,[.,[.,[[.,.],[[.,.],.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[[.,[.,.]],[.,.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[[.,[[.,.],.]],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[.,[.,[.,[[[.,.],[.,.]],.]]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,.]],.],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[.,[.,[.,[[[[.,.],.],.],.]]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[.,[.,[[.,.],.]]],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[.,[[.,.],[.,.]]]],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[.,[.,[[.,.],[.,.]]]],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[.,[.,[[.,.],[.,[.,.]]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[.,[.,[[.,.],[.,[.,[.,.]]]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[.,[.,[[.,.],[.,[[.,.],.]]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [[.,[.,[[.,.],[[.,.],.]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[.,[.,[[.,.],[[.,[.,.]],.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[.,[.,[[.,.],[[[.,.],.],.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,[[.,[.,.]],.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,[[.,[.,.]],.]]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,[[.,[.,.]],[.,.]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[.,[.,[[.,[.,.]],[[.,.],.]]]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,[.,.]]]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,[.,[[.,.],.]]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[.,[.,[[.,[[.,.],.]],[.,.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[.,[.,[[.,[[.,.],[.,.]]],.]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[[.,[[.,[.,.]],.]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[.,[.,[[.,[[[.,.],.],.]],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[.,[.,[[[.,.],.],.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[.,[.,[[[.,.],.],.]]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[.,[.,[[[.,.],.],[.,.]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[.,[.,[[[.,.],.],[[.,.],.]]]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[.,[.,[[[.,.],[.,.]],.]]],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[.,[.,[[[.,.],[.,.]],[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[[[.,.],[.,[.,.]]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[[[.,.],[[.,.],.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[.,[.,[[[.,[.,.]],.],[.,.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[.,[.,[[[.,[.,.]],[.,.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,.]]],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[.,[.,[[[.,[[.,.],.]],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[.,[.,[[[[.,.],.],.],[.,.]]]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[.,[.,[[[[.,.],.],[.,.]],.]]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[.,[.,[[[[.,.],[.,.]],.],.]]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[.,[.,[[[[.,[.,.]],.],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,[[.,.],.]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,[[.,.],.]],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,[[.,.],.]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[.,[[.,.],.]],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,.],.]],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[.,[[.,.],.]],[[.,[.,.]],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,[[.,.],.]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [[.,[[.,.],.]],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [[.,[[.,.],.]],[[[.,[.,.]],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [[.,[[.,.],.]],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[.,[[.,.],[.,.]]],[.,[[.,.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,[[.,.],[.,.]]],[[.,[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[.,[[.,.],[.,.]]],[[[.,.],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,[[.,.],[.,[.,.]]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [[.,[[.,.],[.,[[.,.],.]]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[.,[[.,.],[.,[[.,.],[.,.]]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[.,[[.,.],[.,[[.,[.,.]],.]]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[.,[[.,.],[.,[[[.,.],.],.]]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[[.,.],.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,[[.,.],[[.,[.,.]],[.,.]]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,[[.,.],[[.,[.,[.,.]]],.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],[[.,[[.,.],.]],.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,[[.,.],[[[.,.],.],.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,[[.,.],[[[.,.],.],[.,.]]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,[[.,.],[[[.,.],[.,.]],.]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,[[.,.],[[[.,[.,.]],.],.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[.,[[.,.],[[[[.,.],.],.],.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[.,[[.,[.,.]],.]],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[.,[.,.]],.]],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [[.,[[.,[.,.]],[.,.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[.,[[.,[.,.]],[.,.]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,[[.,[.,.]],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[.,[[.,[.,.]],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[[.,[.,.]],[[.,.],.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,[[.,[.,.]],[[.,.],[.,.]]]],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[[.,[.,.]],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [[.,[[.,[.,[.,.]]],.]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [[.,[[.,[.,[.,.]]],[.,.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,[.,.]]],[[.,.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,[.,.]]]],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[.,[[.,.],.]]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,[.,[[.,.],.]]],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[.,[[.,.],[.,.]]]],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[.,[[.,[.,.]],.]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[.,[[.,[.,[[[.,.],.],.]]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [[.,[[.,[[.,.],.]],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0] => [[.,[[.,[[.,.],.]],[.,.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,[[.,[[.,.],.]],[.,[.,.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[[.,[[.,.],.]],[[.,.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0] => [[.,[[.,[[.,.],[.,.]]],.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[.,[[.,[[.,.],[.,.]]],[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[[.,[[.,.],[.,[.,.]]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],[[.,.],.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,[[.,[[.,[.,.]],[.,.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[.,[[.,[.,[.,.]]],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,[[.,[[.,[[.,.],.]],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[.,[[.,[[[.,.],.],[.,.]]],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,[[.,[[[.,.],[.,.]],.]],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,[[.,[[[.,[.,.]],.],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,[[[[.,.],.],.],.]],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [[.,[[[.,.],.],.]],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[.,[[[.,.],.],.]],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[.,[[[.,.],.],[.,.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[.,[[[.,.],.],[.,.]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[.,[[[.,.],.],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[.,[[[.,.],.],[[.,.],.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],[.,.]]]],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[.,[[[.,.],.],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[.,[[[.,.],.],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0] => [[.,[[[.,.],[.,.]],.]],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[.,[[[.,.],[.,.]],.]],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [[.,[[[.,.],[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[.,[[[.,.],[.,.]],[.,[.,.]]]],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[.,[[[.,.],[.,.]],[[.,.],.]]],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [[.,[[[.,.],[.,[.,.]]],.]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[.,[[[.,.],[.,[.,.]]],[.,.]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,[[[.,.],[.,[.,[.,.]]]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,[[[.,.],[.,[[.,.],.]]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[.,[[[.,.],[[.,.],.]],.]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[.,[[[.,.],[[.,.],.]],[.,.]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[.,[[[.,.],[[.,.],[.,.]]],.]],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],[[.,[.,.]],.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[.,[[[.,.],[[[.,.],.],.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0] => [[.,[[[.,[.,.]],.],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [[.,[[[.,[.,.]],.],.]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],[.,.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[.,[[[.,[.,.]],.],[.,[.,.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[.,[[[.,[.,.]],.],[[.,.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[.,[[[.,[.,.]],[.,.]],.]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],[.,.]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,[.,.]]],.]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[.,[[[.,[.,.]],[[.,.],.]],.]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,[[[.,[.,[.,.]]],.],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,[.,.]]],[.,.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[.,[[[.,[.,[[.,.],.]]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[.,[[[.,[[.,.],.]],.],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[.,[[[.,[[.,.],.]],[.,.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[.,[[[.,[[.,.],[.,.]]],.],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[[[.,[[.,[.,.]],.]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[.,[[[.,[[[.,.],.],.]],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[.,[[[[.,.],.],.],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[.,[[[[.,.],.],.],.]],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[.,[[[[.,.],.],.],[.,.]]],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],[.,[.,.]]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[.,[[[[.,.],.],.],[[.,.],.]]],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[.,[[[[.,.],.],[.,.]],.]],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[.,[[[[.,.],.],[.,.]],[.,.]]],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[.,[[[[.,.],.],[.,[.,.]]],.]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[.,[[[[.,.],.],[[.,.],.]],.]],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[.,[[[[.,.],[.,.]],.],.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,[[[[.,.],[.,.]],.],[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[.,[[[[.,.],[.,.]],[.,.]],.]],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],[.,[.,.]]],.],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[.,[[[[.,.],[[.,.],.]],.],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,[[[[.,[.,.]],.],.],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[.,[[[[.,[.,.]],.],[.,.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,[[[[.,[.,.]],[.,.]],.],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,[[[[.,[.,[.,.]]],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[[[.,[[.,.],.]],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,[[[[[.,.],.],.],.],[.,.]]],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[.,[[[[[.,.],.],.],[.,.]],.]],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,[[[[[.,.],.],[.,.]],.],.]],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[.,[[[[[.,.],[.,.]],.],.],.]],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,[[[[[.,[.,.]],.],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[[.,.],.],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [[[.,.],.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[[.,.],.],[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[[.,.],.],[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [[[.,.],.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [[[.,.],.],[[[.,.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],.],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [[[.,.],.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [[[.,.],.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,.],[.,.]],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,.],[.,.]],[[.,.],[.,[.,.]]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[.,.]],[[.,.],[[.,.],.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,.],[.,.]],[[.,[.,.]],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [[[.,.],[.,.]],[[[.,.],.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[[.,.],[.,[.,.]]],[.,[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[[.,.],[.,[.,.]]],[[.,[.,.]],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [[[.,.],[.,[.,.]]],[[[.,.],.],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,.]]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [[[.,.],[.,[.,[.,[[.,.],.]]]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0] => [[[.,.],[.,[.,[[.,.],.]]]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [[[.,.],[.,[.,[[.,[.,.]],.]]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0] => [[[.,.],[.,[.,[[[.,.],.],.]]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[[.,.],.]]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0] => [[[.,.],[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0] => [[[.,.],[.,[[.,[.,[.,.]]],.]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0] => [[[.,.],[.,[[.,[[.,.],.]],.]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0] => [[[.,.],[.,[[[.,.],.],.]]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [[[.,.],[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,.],[.,[[[.,.],[.,.]],.]]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [[[.,.],[.,[[[.,[.,.]],.],.]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [[[.,.],[.,[[[[.,.],.],.],.]]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],[[.,.],.]],[.,[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],[[.,.],.]],[.,[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[[.,.],.]],[[.,.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,[.,.]],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [[[.,.],[[.,.],.]],[[[.,.],.],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[[.,.],[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,.],[.,.]]],[[.,.],.]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[.,.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[[.,.],[.,[.,[.,.]]]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [[[.,.],[[.,.],[.,[[.,.],.]]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [[[.,.],[[.,.],[[.,.],.]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [[[.,.],[[.,.],[[.,.],[.,.]]]],.] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [[[.,.],[[.,.],[[.,[.,.]],.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0] => [[[.,.],[[.,.],[[[.,.],.],.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,.],[[.,[.,.]],.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],[[.,[.,.]],[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0] => [[[.,.],[[.,[.,.]],[[.,.],.]]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],[[.,[.,[.,.]]],[.,.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],[[.,[.,[[.,.],.]]],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,.],[[.,[[.,.],.]],.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [[[.,.],[[.,[[.,.],.]],[.,.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [[[.,.],[[.,[[.,.],[.,.]]],.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],[[.,[[.,[.,.]],.]],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],[[.,[[[.,.],.],.]],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],[[[.,.],.],.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],[[[.,.],.],.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],[[[.,.],.],[.,.]]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [[[.,.],[[[.,.],.],[[.,.],.]]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [[[.,.],[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [[[.,.],[[[.,.],[.,.]],[.,.]]],.] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0] => [[[.,.],[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [[[.,.],[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],[[[.,[.,.]],.],[.,.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [[[.,.],[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],[[[.,[.,[.,.]]],.],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [[[.,.],[[[.,[[.,.],.]],.],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [[[.,.],[[[[.,.],.],.],.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],[[[[.,.],.],.],[.,.]]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [[[.,.],[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],[[[[.,.],[.,.]],.],.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],[[[[.,[.,.]],.],.],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],[[[[[.,.],.],.],.],.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,.]],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,.]],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [[[.,[.,.]],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [[[.,[.,.]],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],[[.,[.,.]],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [[[.,[.,.]],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[.,[.,.]],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [[[.,[.,.]],.],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [[[.,[.,.]],.],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[.,[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[.,.]],[.,.]],[[.,.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[.,.]],[[.,[.,.]],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,.],.],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [[[.,[.,.]],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [[[.,[.,.]],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [[[.,[.,.]],[.,[[.,.],[.,.]]]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [[[.,[.,.]],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[[.,.],.]],[.,[.,.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[[.,.],.]],[[.,.],.]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[.,[.,.]],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0] => [[[.,[.,.]],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [[[.,[.,.]],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [[[.,[.,.]],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],[[[.,.],[.,.]],.]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [[[.,[.,.]],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],[[[[.,.],.],.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [[[.,[.,[.,.]]],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,[.,.]]],.],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [[[.,[.,[.,.]]],[.,.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0] => [[[.,[.,[.,.]]],[.,[[.,.],.]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[[.,.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[[.,.],[.,.]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[[.,[.,.]],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0] => [[[.,[.,[.,.]]],[[[.,.],.],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[.,[[.,.],[.,.]]]]],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [[[.,[.,[[.,.],.]]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[.,[[.,.],.]]],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,[[.,.],[.,.]]]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,[[.,.],[.,.]]]],[.,.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[.,[[.,.],[.,[.,.]]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],[[.,.],.]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[.,[[.,[.,.]],[.,.]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0] => [[[.,[.,[[.,[[.,.],.]],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [[[.,[.,[[[.,.],.],[.,.]]]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [[[.,[[.,.],.]],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [[[.,[[.,.],.]],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [[[.,[[.,.],.]],.],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [[[.,[[.,.],.]],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [[[.,[[.,.],.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [[[.,[[.,.],.]],[.,[[.,.],.]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [[[.,[[.,.],.]],[[.,.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [[[.,[[.,.],.]],[[.,.],[.,.]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [[[.,[[.,.],.]],[[.,[.,.]],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [[[.,[[.,.],.]],[[[.,.],.],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0] => [[[.,[[.,.],[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [[[.,[[.,.],[.,.]]],.],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [[[.,[[.,.],[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [[[.,[[.,.],[.,.]]],[[.,.],.]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [[[.,[[.,.],[.,[.,.]]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [[[.,[[.,.],[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [[[.,[[.,.],[.,[.,[.,.]]]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[[.,[[.,.],[.,[[.,.],.]]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],[[.,.],.]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],[[.,.],.]]],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [[[.,[[.,.],[[.,.],[.,.]]]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [[[.,[[.,.],[[.,[.,.]],.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [[[.,[[.,.],[[[.,.],.],.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [[[.,[[.,[.,.]],.]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [[[.,[[.,[.,.]],.]],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [[[.,[[.,[.,.]],.]],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [[[.,[[.,[.,.]],[.,.]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],[.,.]]],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [[[.,[[.,[.,.]],[.,[.,.]]]],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [[[.,[[.,[.,.]],[[.,.],.]]],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [[[.,[[.,[.,[.,.]]],[.,.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[.,[[.,.],.]]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [[[.,[[.,[[.,.],.]],.]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [[[.,[[.,[[.,.],.]],[.,.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [[[.,[[.,[[.,.],[.,.]]],.]],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [[[.,[[.,[[[.,.],.],.]],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,[[[.,.],.],.]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,[[[.,.],.],.]],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [[[.,[[[.,.],.],.]],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [[[.,[[[.,.],.],.]],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [[[.,[[[.,.],.],[.,.]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [[[.,[[[.,.],.],[.,.]]],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [[[.,[[[.,.],.],[.,[.,.]]]],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [[[.,[[[.,.],.],[[.,.],.]]],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [[[.,[[[.,.],[.,.]],.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [[[.,[[[.,.],[.,.]],[.,.]]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [[[.,[[[.,.],[[.,.],.]],.]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [[[.,[[[.,[.,.]],.],[.,.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [[[.,[[[[.,.],.],.],[.,.]]],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [[[.,[[[[.,.],[.,.]],.],.]],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [[[[.,.],.],.],[[.,[.,.]],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [[[[.,.],.],[.,.]],[.,[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],.],[.,.]],[[.,.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,4),(4,7),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,.],.],[.,.]],[[.,[.,.]],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [[[[.,.],.],[.,.]],[[[.,.],.],.]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [[[[.,.],.],[.,[.,.]]],[[.,.],.]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [[[[.,.],.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [[[[.,.],.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [[[[.,.],.],[.,[[.,.],[.,.]]]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [[[[.,.],.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [[[[.,.],.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],.],[[.,.],.]],[.,[.,.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],.],[[.,.],.]],[[.,.],.]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [[[[.,.],.],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [[[[.,.],.],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [[[[.,.],.],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0] => [[[[.,.],.],[[[.,.],[.,.]],.]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [[[[.,.],[.,.]],.],[.,[[.,.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],.],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[[.,.],[.,.]],.],[[.,[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[.,.],[.,.]],.],[[[.,.],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],.]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0] => [[[[.,.],[.,.]],[.,[[.,.],.]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[[.,.],[.,.]]],.] => ([(0,6),(1,6),(2,5),(3,5),(5,7),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[[[.,.],[.,.]],[[.,[.,.]],.]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [[[[.,.],[.,.]],[[[.,.],.],.]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [[[[.,.],[.,[.,.]]],.],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[[.,.],[.,[.,.]]],[[.,.],.]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],[.,[.,[[.,.],.]]]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [[[[.,.],[.,[[.,.],.]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0] => [[[[.,.],[.,[[.,.],.]]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[[[.,.],[.,[[.,.],[.,.]]]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [[[[.,.],[.,[[.,[.,.]],.]]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [[[[.,.],[.,[[[.,.],.],.]]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],[[.,.],.]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],[[.,.],.]],.],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],[[.,.],.]],[.,[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[[.,.],[[.,.],.]],[[.,.],.]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [[[[.,.],[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [[[[.,.],[[.,.],[.,.]]],[.,.]],.] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[[[.,.],[[.,.],[.,[.,.]]]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[[.,.],[[.,.],[[.,.],.]]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],[[.,[.,.]],.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[[.,.],[[.,[.,.]],[.,.]]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,[.,.]]],.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [[[[.,.],[[.,[[.,.],.]],.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [[[[.,.],[[[.,.],.],.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [[[[.,.],[[[.,.],.],.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [[[[.,.],[[[.,.],.],[.,.]]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [[[[.,.],[[[.,.],[.,.]],.]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [[[[.,.],[[[.,[.,.]],.],.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],[[[[.,.],.],.],.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [[[[.,[.,.]],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],.],.],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [[[[.,[.,.]],.],[.,[[.,.],.]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [[[[.,[.,.]],.],[[.,.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [[[[.,[.,.]],.],[[.,.],[.,.]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[[[.,[.,.]],.],[[.,[.,.]],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],[[[.,.],.],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [[[[.,[.,.]],[.,.]],.],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,[.,.]],[.,.]],[[.,.],.]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,[.,.]],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [[[[.,[.,.]],[[.,.],.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [[[[.,[.,.]],[[.,.],.]],[.,.]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,[.,.]],[[.,.],[.,.]]],.],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [[[[.,[.,.]],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [[[[.,[.,[.,.]]],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,[.,[.,.]]],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,.]]],[[.,.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[[.,.],.]]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [[[[.,[.,[[.,.],.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [[[[.,[.,[[.,.],.]]],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [[[[.,[.,[[.,.],[.,.]]]],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [[[[.,[.,[[.,[.,.]],.]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [[[[.,[.,[[[.,.],.],.]]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [[[[.,[[.,.],.]],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [[[[.,[[.,.],.]],.],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [[[[.,[[.,.],.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [[[[.,[[.,.],.]],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [[[[.,[[.,.],.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [[[[.,[[.,.],.]],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [[[[.,[[.,.],.]],[.,[.,.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],[[.,.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [[[[.,[[.,.],[.,.]]],.],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,[[.,.],[.,.]]],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [[[[.,[[.,.],[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [[[[.,[[.,.],[.,[.,.]]]],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [[[[.,[[.,.],[[.,.],.]]],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[[[.,[[.,[.,.]],.]],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [[[[.,[[.,[.,.]],[.,.]]],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,[.,.]]],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[[[.,[[.,[[.,.],.]],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [[[[.,[[[.,.],.],.]],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [[[[.,[[[.,.],.],[.,.]]],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [[[[.,[[[.,.],[.,.]],.]],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [[[[.,[[[.,[.,.]],.],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,[[[[.,.],.],.],.]],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [[[[[.,.],.],.],[.,.]],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [[[[[.,.],.],.],[.,[[.,.],.]]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [[[[[.,.],.],.],[[.,.],.]],[.,.]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [[[[[.,.],.],.],[[.,.],[.,.]]],.] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [[[[[.,.],.],.],[[.,[.,.]],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [[[[[.,.],.],.],[[[.,.],.],.]],.] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [[[[[.,.],.],[.,.]],.],[[.,.],.]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [[[[[.,.],.],[.,.]],[[.,.],.]],.] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [[[[[.,.],.],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [[[[[.,.],.],[[.,.],.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [[[[[.,.],.],[[.,.],.]],[.,.]],.] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [[[[[.,.],.],[[.,.],[.,.]]],.],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [[[[[.,.],.],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [[[[[.,.],.],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [[[[[.,.],[.,.]],.],.],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [[[[[.,.],[.,.]],.],[[.,.],.]],.] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [[[[[.,.],[.,.]],[[.,.],.]],.],.] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [[[[[.,.],[.,[[.,.],.]]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [[[[[.,.],[[.,.],.]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [[[[[.,.],[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [[[[[.,.],[[.,.],.]],[.,.]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[[.,.],[.,.]]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [[[[[.,.],[[.,[.,.]],.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [[[[[.,.],[[[.,.],.],.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [[[[[.,[.,.]],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [[[[[.,[.,.]],.],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [[[[[.,[.,.]],.],[[.,.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [[[[[.,[.,.]],[[.,.],.]],.],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[[.,.],.]]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [[[[[.,[[.,.],.]],.],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[[[.,[[.,.],[.,.]]],.],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[[[.,[[.,[.,.]],.]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [[[[[.,[[[.,.],.],.]],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [[[[[[.,.],.],.],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [[[[[[.,.],.],.],[[.,.],.]],.],.] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [[[[[[.,.],.],[[.,.],.]],.],.],.] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[.,.],[[.,.],.]],.],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[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),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],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),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => ([(0,9),(1,9),(2,8),(3,8),(4,5),(5,7),(6,4),(7,3),(9,6)],10)
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[[.,[[[[.,.],.],.],.]],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],[.,.]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [[[[[[.,[.,.]],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],[[.,.],.]],.],.],.],.]] => ([(0,4),(1,3),(3,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,8)],10)
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => ([(0,9),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5),(8,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0] => [[[[[[.,.],[.,.]],.],.],.],[[.,.],.]] => ([(0,8),(1,8),(2,4),(3,7),(4,7),(5,6),(6,3),(8,5)],9)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],.],.]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,[.,[[[[[[.,.],.],.],.],.],.]]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,[[.,.],[[[[[.,.],.],.],.],.]]],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[.,[[[[[[.,.],.],.],.],.],[.,.]]],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,[[[[[[.,.],[.,.]],.],.],.],.]],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,[[[[[[[.,.],.],.],.],.],.],.]],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],[[[[[[.,.],.],.],.],.],.]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,[.,[[[[[.,.],.],.],.],.]]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [[[.,[[[[[.,.],.],.],.],[.,.]]],.],.] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[.,[[[[[[.,.],.],.],.],.],.]],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,0] => [[[[.,.],[.,.]],[[.,.],[[.,.],.]]],.] => ([(0,8),(1,6),(2,6),(3,5),(5,8),(6,7),(7,4),(8,7)],9)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,.],[[.,[.,[.,[.,.]]]],.]],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.] => ([(0,7),(1,6),(3,8),(4,8),(5,2),(6,3),(7,4),(8,5)],9)
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],[[.,.],.]],.],.] => ([(0,7),(1,4),(3,8),(4,8),(5,3),(6,2),(7,5),(8,6)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [[[[.,[.,[[[[.,.],.],.],.]]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0,0] => [[[[.,[[.,[.,[.,.]]],.]],[.,.]],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[.,[[.,[.,[.,[.,.]]]],.]],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[.,[[[[.,.],.],.],[.,.]]],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,7),(2,8),(3,8),(5,2),(6,3),(7,5),(8,4)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[.,.],[.,[.,[.,.]]]],[.,.]],.],.] => ([(0,8),(1,7),(2,5),(4,7),(5,4),(6,3),(7,8),(8,6)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[[.,.],.]]]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [[[[[.,[.,[[[.,.],.],.]]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[.,[[.,[.,[.,.]]],.]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[[[[.,[[.,[[.,.],.]],.]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [[[[[.,[[[.,.],.],[.,.]]],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[.,[[[[.,.],.],.],.]],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,7),(2,8),(3,8),(5,2),(6,3),(7,5),(8,4)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [[[[[[.,.],[[.,[.,.]],.]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [[[[[[.,.],[[[.,.],.],.]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],[[.,.],.]],.],.],.],.] => ([(0,4),(1,3),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [[[[[[.,[.,[[.,.],.]]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[.,[[.,.],.]],.],.],.],[.,.]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [[[[[[.,[[.,.],.]],[.,.]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [[[[[[.,[[.,.],[.,.]]],.],.],.],.],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[.,[[.,[.,.]],.]],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [[[[[[[.,.],.],[[.,.],.]],.],.],.],.] => ([(0,4),(1,3),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] => ([(0,8),(1,7),(2,7),(4,8),(5,4),(6,5),(7,6),(8,3)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [[[[[[[.,.],[.,.]],[.,.]],.],.],.],.] => ([(0,8),(1,7),(2,7),(4,6),(5,4),(6,3),(7,8),(8,5)],9)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],[[.,.],.]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[[.,.],.]],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]] => ([(0,7),(1,4),(3,8),(4,8),(5,2),(6,5),(7,3),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.] => ([(0,8),(1,7),(2,9),(3,9),(5,2),(6,3),(7,5),(8,6),(9,4)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]] => ([(0,8),(1,8),(2,7),(4,7),(5,4),(6,3),(7,6),(8,5)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]] => ([(0,7),(1,4),(3,8),(4,8),(5,3),(6,2),(7,5),(8,6)],9)
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => ([(0,8),(1,7),(2,7),(4,6),(5,4),(6,3),(7,8),(8,5)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,6),(4,7),(5,4),(6,5),(7,8),(8,3)],9)
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,7),(2,8),(3,8),(5,2),(6,3),(7,5),(8,4)],9)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [.,[[[[[.,.],.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,7),(2,8),(3,8),(5,2),(6,3),(7,5),(8,4)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,8),(1,5),(2,6),(3,8),(4,7),(5,7),(6,3),(8,4)],9)
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => [[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,8),(1,5),(2,6),(3,7),(4,7),(5,8),(6,4),(8,3)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,9),(3,7),(4,8),(6,8),(7,9),(8,7),(9,5)],10)
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => ([(0,8),(1,4),(2,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,3)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[[.,.],.]]]]],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.],.] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0] => [[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => ([(0,10),(1,8),(3,10),(4,5),(5,3),(6,7),(7,2),(8,4),(9,6),(10,9)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [[[[[[[.,[.,[[.,.],.]]],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.],.] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => ([(0,10),(1,9),(2,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7),(10,3)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,4),(3,7),(4,8),(5,3),(6,5),(7,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,7),(1,5),(2,6),(3,8),(4,7),(5,3),(6,4),(7,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,4),(3,8),(4,7),(5,3),(6,5),(7,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,8),(2,6),(3,7),(4,5),(5,3),(6,4),(8,7)],9)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [[[.,[.,.]],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [[[[.,[.,.]],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,7),(2,8),(3,8),(5,2),(6,3),(7,5),(8,4)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,4),(3,8),(4,8),(5,3),(6,2),(7,5),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]] => ([(0,4),(1,3),(3,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,.]]]],[.,[.,[[.,.],.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]],.] => ([(0,8),(1,7),(3,9),(4,9),(5,3),(6,2),(7,5),(8,4),(9,6)],10)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]],.] => ([(0,8),(1,4),(3,9),(4,9),(5,3),(6,2),(7,6),(8,5),(9,7)],10)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [[.,[.,[.,[.,.]]]],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[.,[.,.]]],[[[[.,[.,.]],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,[.,.]],[[[[.,[.,[.,.]]],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[[[[.,[.,[.,[.,.]]]],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0] => [[[[.,[[.,.],.]],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,1,0,0,0] => [[[[[.,.],.],[.,.]],.],[[[.,.],.],.]] => ([(0,8),(1,5),(2,6),(3,7),(4,7),(5,8),(6,4),(8,3)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]] => ([(0,4),(1,3),(3,8),(4,8),(5,6),(6,2),(7,5),(8,7)],9)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(3,7),(4,8),(5,3),(6,5),(7,8)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,9),(1,7),(2,4),(3,5),(4,9),(5,6),(6,8),(7,8),(9,7)],10)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]] => ([(0,9),(1,7),(2,5),(3,6),(4,8),(5,9),(6,7),(7,8),(9,4)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]] => ([(0,8),(1,7),(2,4),(3,5),(4,9),(5,8),(6,9),(7,6),(8,7)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.] => ([(0,8),(1,9),(2,7),(3,4),(4,9),(5,6),(7,8),(8,5),(9,7)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,.],[[.,.],[.,.]]]]],[.,.]] => ([(0,7),(1,8),(2,9),(3,6),(4,6),(5,9),(6,7),(7,8),(8,5)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[[.,.],[.,.]]]],[[.,.],[.,.]]] => ([(0,8),(1,6),(2,6),(3,7),(4,7),(5,9),(6,8),(7,9),(8,5)],10)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,.],[.,.]]],[[.,.],[[.,.],[.,.]]]] => ([(0,7),(1,8),(2,8),(3,6),(4,6),(5,9),(6,7),(7,9),(8,5)],10)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,8),(4,5),(5,9),(6,8),(7,9),(8,7)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => ([(0,8),(1,4),(3,9),(4,9),(5,6),(6,2),(7,5),(8,3),(9,7)],10)
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => ([(0,8),(1,4),(3,9),(4,9),(5,3),(6,5),(7,2),(8,6),(9,7)],10)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => ([(0,8),(1,7),(3,9),(4,9),(5,3),(6,2),(7,5),(8,4),(9,6)],10)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => ([(0,8),(1,7),(2,5),(3,9),(5,8),(6,4),(7,3),(8,9),(9,6)],10)
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => ([(0,8),(1,9),(2,5),(4,8),(5,9),(6,4),(7,3),(8,7),(9,6)],10)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => ([(0,9),(1,7),(2,5),(4,8),(5,8),(6,3),(7,4),(8,9),(9,6)],10)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => ([(0,9),(1,8),(2,7),(4,8),(5,4),(6,3),(7,5),(8,9),(9,6)],10)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => ([(0,8),(1,9),(2,7),(3,4),(4,9),(5,6),(7,8),(8,5),(9,7)],10)
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,7),(3,9),(4,8),(5,9),(6,8),(7,3),(9,4)],10)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => ([(0,9),(1,7),(2,5),(3,9),(4,8),(5,8),(6,3),(7,6),(9,4)],10)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => ([(0,8),(1,7),(2,4),(3,5),(4,9),(5,8),(6,9),(7,6),(8,7)],10)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => ([(0,9),(1,7),(2,5),(3,8),(4,8),(5,9),(6,4),(7,6),(9,3)],10)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => ([(0,8),(1,7),(2,4),(3,9),(4,8),(5,6),(6,3),(7,5),(8,9)],10)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => ([(0,9),(1,7),(2,5),(3,6),(4,8),(5,9),(6,7),(7,8),(9,4)],10)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => ([(0,9),(1,7),(2,5),(3,8),(4,8),(5,9),(6,4),(7,3),(9,6)],10)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => ([(0,5),(1,6),(2,7),(3,9),(4,8),(5,8),(6,3),(7,4),(8,9)],10)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => ([(0,8),(1,6),(2,7),(3,9),(4,8),(5,4),(6,5),(7,3),(8,9)],10)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => ([(0,9),(1,7),(2,4),(3,5),(4,9),(5,6),(6,8),(7,8),(9,7)],10)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.]] => ([(0,11),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,1),(11,9)],12)
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]],.]] => ([(0,10),(1,4),(3,11),(4,11),(5,6),(6,8),(7,5),(8,2),(9,7),(10,3),(11,9)],12)
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[.,[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]],.]] => ([(0,10),(1,4),(3,11),(4,11),(5,3),(6,8),(7,5),(8,2),(9,6),(10,7),(11,9)],12)
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.]] => ([(0,10),(1,9),(3,11),(4,11),(5,2),(6,5),(7,4),(8,6),(9,7),(10,3),(11,8)],12)
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[.,[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]],.]] => ([(0,10),(1,9),(2,5),(4,11),(5,10),(6,8),(7,6),(8,3),(9,4),(10,11),(11,7)],12)
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [.,[[[.,[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => ([(0,10),(1,4),(3,11),(4,11),(5,7),(6,5),(7,3),(8,6),(9,2),(10,8),(11,9)],12)
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => ([(0,7),(1,9),(2,6),(3,11),(5,10),(6,11),(7,10),(8,4),(9,3),(10,8),(11,5)],12)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]],.]] => ([(0,9),(1,10),(3,11),(4,11),(5,6),(6,3),(7,4),(8,2),(9,7),(10,5),(11,8)],12)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => ([(0,10),(1,9),(2,5),(4,11),(5,10),(6,7),(7,4),(8,3),(9,6),(10,11),(11,8)],12)
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]],.]] => ([(0,10),(1,9),(3,11),(4,11),(5,7),(6,5),(7,4),(8,2),(9,6),(10,3),(11,8)],12)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],.]] => ([(0,11),(1,9),(2,6),(4,10),(5,10),(6,11),(7,5),(8,3),(9,4),(10,8),(11,7)],12)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => ([(0,6),(1,8),(2,9),(4,11),(5,10),(6,10),(7,3),(8,4),(9,5),(10,11),(11,7)],12)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],.]] => ([(0,10),(1,9),(2,8),(4,11),(5,10),(6,5),(7,3),(8,6),(9,4),(10,11),(11,7)],12)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],.]] => ([(0,11),(1,10),(2,8),(3,6),(4,9),(6,10),(7,5),(8,4),(9,7),(10,11),(11,9)],12)
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[.,.]],.]] => ([(0,11),(1,9),(3,11),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7),(10,2),(11,10)],12)
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => [.,[[[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,5),(4,11),(5,10),(6,7),(7,4),(8,6),(9,3),(10,8),(11,9)],12)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[.,.]],.]] => ([(0,11),(1,9),(2,6),(4,10),(5,11),(6,10),(7,5),(8,3),(9,4),(10,7),(11,8)],12)
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,7),(4,10),(5,11),(6,4),(7,6),(8,3),(9,5),(10,9),(11,8)],12)
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]] => ([(0,11),(1,9),(2,10),(3,6),(5,10),(6,9),(7,4),(8,5),(9,11),(10,7),(11,8)],12)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => ([(0,11),(1,9),(2,5),(4,10),(5,10),(6,4),(7,6),(8,3),(9,7),(10,11),(11,8)],12)
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,7),(3,5),(5,11),(6,9),(7,9),(8,4),(9,10),(10,8),(11,6)],12)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]] => ([(0,11),(1,9),(2,8),(4,10),(5,10),(6,3),(7,5),(8,7),(9,4),(10,11),(11,6)],12)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,6),(3,7),(5,9),(6,10),(7,5),(8,4),(9,11),(10,9),(11,8)],12)
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => [.,[[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[.,.]],.]] => ([(0,11),(1,10),(2,9),(4,10),(5,7),(6,5),(7,4),(8,3),(9,6),(10,11),(11,8)],12)
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]] => ([(0,11),(1,9),(2,10),(3,6),(5,9),(6,10),(7,5),(8,4),(9,11),(10,7),(11,8)],12)
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]] => ([(0,11),(1,10),(2,6),(3,7),(5,9),(6,9),(7,5),(8,4),(9,10),(10,11),(11,8)],12)
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]] => ([(0,10),(1,11),(2,9),(3,8),(5,9),(6,5),(7,4),(8,6),(9,10),(10,11),(11,7)],12)
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]] => ([(0,9),(1,10),(2,11),(3,8),(4,5),(5,11),(6,7),(8,9),(9,10),(10,6),(11,8)],12)
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[.,[.,.]],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]] => ([(0,10),(1,3),(2,11),(3,11),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8)],12)
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],.]] => ([(0,9),(1,5),(2,6),(3,11),(4,10),(5,10),(6,11),(7,4),(8,7),(9,3),(11,8)],12)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[.,.]],[[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],.]] => ([(0,6),(1,9),(2,5),(3,11),(4,10),(5,11),(6,10),(7,8),(8,3),(9,7),(11,4)],12)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]] => ([(0,6),(1,8),(2,9),(3,11),(4,11),(5,10),(6,10),(7,3),(8,4),(9,7),(11,5)],12)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],.]] => ([(0,10),(1,6),(2,7),(3,8),(4,11),(5,9),(6,9),(7,10),(8,4),(10,11),(11,5)],12)
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [[.,[.,.]],[[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],.]] => ([(0,11),(1,9),(2,5),(3,11),(4,10),(5,10),(6,8),(7,6),(8,3),(9,7),(11,4)],12)
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,7),(3,5),(4,11),(5,10),(6,9),(7,9),(8,4),(10,8),(11,6)],12)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [[.,[.,.]],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]] => ([(0,11),(1,6),(2,7),(3,8),(4,9),(5,10),(6,9),(7,10),(8,5),(10,11),(11,4)],12)
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]] => ([(0,10),(1,11),(2,8),(3,6),(4,10),(5,9),(6,9),(7,4),(8,7),(10,11),(11,5)],12)
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[.,.]],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]] => ([(0,9),(1,10),(2,8),(3,6),(4,7),(5,11),(6,11),(7,10),(8,9),(9,5),(10,8)],12)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[.,[.,.]],.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => ([(0,9),(1,10),(2,11),(3,11),(4,5),(5,7),(6,4),(7,3),(8,2),(9,8),(10,6)],12)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => ([(0,6),(1,8),(2,9),(3,11),(4,10),(5,10),(6,11),(7,4),(8,3),(9,7),(11,5)],12)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => ([(0,11),(1,8),(2,9),(3,10),(4,11),(5,10),(6,3),(7,4),(8,6),(9,7),(11,5)],12)
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => ([(0,10),(1,11),(2,8),(3,4),(4,10),(5,9),(6,9),(7,6),(8,7),(10,11),(11,5)],12)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,.]],[.,.]],[[.,[[.,[[.,[.,.]],.]],.]],.]] => ([(0,10),(1,9),(2,4),(3,11),(4,10),(5,6),(6,8),(7,5),(8,3),(9,7),(10,11)],12)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[[[.,[.,.]],[[.,[.,.]],.]],.]] => ([(0,9),(1,7),(2,6),(3,8),(4,10),(5,11),(6,11),(7,9),(8,5),(9,10),(11,4)],12)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[.,[[.,[.,.]],.]],[.,.]],.]] => ([(0,10),(1,11),(2,8),(3,5),(4,11),(5,10),(6,9),(7,4),(8,7),(10,9),(11,6)],12)
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]] => ([(0,8),(1,9),(2,10),(3,6),(4,7),(5,11),(6,9),(7,10),(8,5),(9,11),(10,8)],12)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[.,[[.,[.,.]],.]],.]] => ([(0,9),(1,10),(2,11),(3,11),(4,8),(5,4),(6,7),(7,2),(8,3),(9,5),(10,6)],12)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[[[.,[.,.]],[.,.]],.]] => ([(0,11),(1,9),(2,5),(3,10),(4,10),(5,11),(6,8),(7,6),(8,3),(9,7),(11,4)],12)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => ([(0,11),(1,9),(2,5),(3,10),(4,10),(5,11),(6,7),(7,3),(8,4),(9,6),(11,8)],12)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[[.,[.,.]],[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => ([(0,10),(1,11),(2,4),(3,5),(4,10),(5,11),(6,9),(7,9),(8,7),(10,8),(11,6)],12)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[.,[[.,[.,.]],.]],.]] => ([(0,8),(1,9),(2,5),(3,11),(4,10),(5,10),(6,7),(7,3),(8,6),(9,4),(10,11)],12)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]] => ([(0,11),(1,7),(2,6),(3,8),(4,10),(5,9),(6,11),(7,9),(8,5),(9,10),(11,4)],12)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => ([(0,10),(1,8),(2,9),(3,11),(4,10),(5,7),(6,4),(7,3),(8,5),(9,6),(10,11)],12)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => ([(0,10),(1,11),(2,8),(3,5),(4,10),(5,11),(6,9),(7,4),(8,7),(10,9),(11,6)],12)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[.,[[.,[.,.]],.]],.]] => ([(0,11),(1,10),(2,8),(3,5),(4,9),(5,10),(6,7),(7,4),(8,6),(10,11),(11,9)],12)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]] => ([(0,11),(1,8),(2,9),(3,7),(4,5),(5,11),(6,10),(7,9),(8,10),(9,8),(11,6)],12)
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],[[.,[.,.]],.]] => ([(0,10),(1,9),(2,11),(3,11),(4,6),(5,4),(6,8),(7,5),(8,3),(9,7),(10,2)],12)
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[.,[[[.,[.,.]],[.,.]],.]],.]],[[.,[.,.]],.]] => ([(0,11),(1,9),(2,5),(3,10),(4,10),(5,11),(6,8),(7,6),(8,3),(9,4),(11,7)],12)
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[.,[[[.,[.,.]],[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => ([(0,6),(1,8),(2,9),(3,10),(4,10),(5,11),(6,11),(7,3),(8,4),(9,5),(11,7)],12)
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]] => ([(0,11),(1,9),(2,8),(3,11),(4,10),(5,10),(6,3),(7,5),(8,6),(9,4),(11,7)],12)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[[.,[.,.]],.]] => ([(0,11),(1,10),(2,6),(3,7),(4,9),(5,9),(6,10),(7,5),(8,4),(10,11),(11,8)],12)
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[.,[[.,[.,.]],.]],.]],[[.,[.,.]],.]] => ([(0,9),(1,8),(2,5),(3,11),(4,10),(5,10),(6,4),(7,6),(8,7),(9,3),(10,11)],12)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]] => ([(0,11),(1,7),(2,6),(3,8),(4,10),(5,9),(6,11),(7,9),(8,4),(9,10),(11,5)],12)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => ([(0,7),(1,8),(2,9),(3,11),(4,10),(5,10),(6,5),(7,3),(8,6),(9,4),(10,11)],12)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]] => ([(0,9),(1,6),(2,7),(3,8),(4,10),(5,11),(6,9),(7,4),(8,5),(9,11),(11,10)],12)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[.,[[.,[.,.]],.]],.]],[.,.]],[[.,[.,.]],.]] => ([(0,10),(1,9),(2,8),(3,11),(4,10),(5,6),(6,4),(7,5),(8,7),(9,3),(10,11)],12)
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[[.,[.,.]],.]] => ([(0,10),(1,11),(2,6),(3,7),(4,9),(5,11),(6,10),(7,4),(8,5),(10,8),(11,9)],12)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]] => ([(0,11),(1,6),(2,7),(3,8),(4,9),(5,10),(6,9),(7,4),(8,5),(9,11),(11,10)],12)
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[[.,[.,.]],.]] => ([(0,11),(1,10),(2,7),(3,8),(4,9),(5,10),(6,5),(7,6),(8,4),(10,11),(11,9)],12)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]] => ([(0,8),(1,11),(2,10),(3,5),(4,6),(5,11),(6,7),(7,9),(8,10),(10,9),(11,8)],12)
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,[[[[[.,.],.],.],.],.]],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[.,[[[[.,.],.],.],.]],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => ([(0,9),(1,3),(2,10),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],[.,[[.,.],[.,[.,.]]]]] => ([(0,8),(1,5),(2,6),(3,7),(4,7),(5,8),(6,4),(8,3)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.] => ([(0,8),(1,7),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2),(9,4)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.] => ([(0,8),(1,4),(3,9),(4,9),(5,3),(6,5),(7,2),(8,6),(9,7)],10)
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,[.,.]],.],.],.],.],.]]]]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,[[[[.,[.,.]],.],.],.]],.]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [.,[.,[[.,[[[[.,.],.],.],.]],[.,.]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,7),(2,6),(4,8),(5,4),(6,5),(7,8),(8,3)],9)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[.,.]],[.,.]],[[.,.],[[.,.],.]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(7,6),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [.,[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [.,[[[[[[.,.],.],.],.],[[.,.],.]],.]] => ([(0,7),(1,4),(3,8),(4,8),(5,3),(6,2),(7,5),(8,6)],9)
[1,1,0,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],[[.,.],.]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(7,6),(8,6)],9)
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,.],.]],[.,.]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,7),(3,4),(4,5),(5,7),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,9),(1,8),(2,7),(3,8),(4,6),(5,4),(6,3),(7,5),(8,9)],10)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,.]]],[.,[.,[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]] => ([(0,7),(1,8),(2,8),(3,9),(4,6),(5,9),(6,7),(8,5),(9,6)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => ([(0,8),(1,9),(2,7),(3,5),(5,6),(6,7),(7,8),(8,9),(9,4)],10)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]] => ([(0,9),(1,7),(2,5),(3,8),(4,8),(5,9),(6,4),(7,6),(9,3)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]] => ([(0,9),(1,7),(2,8),(3,4),(4,9),(6,8),(7,5),(8,7),(9,6)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[[.,.],.]]] => ([(0,6),(1,6),(2,9),(3,8),(4,5),(5,9),(6,8),(8,7),(9,7)],10)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],.]] => ([(0,7),(1,8),(2,8),(3,6),(4,6),(5,9),(6,7),(7,9),(8,5)],10)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0] => [[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],.] => ([(0,8),(1,6),(2,6),(3,7),(4,7),(6,8),(7,9),(8,9),(9,5)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => ([(0,7),(1,11),(2,9),(3,10),(4,8),(5,6),(6,11),(7,10),(9,8),(10,9),(11,7)],12)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]] => ([(0,7),(1,10),(2,10),(3,11),(4,8),(5,9),(6,11),(7,9),(9,8),(10,6),(11,7)],12)
[1,1,0,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[.,[.,.]],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0,1,0] => [[[[.,.],.],[[.,.],.]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,5),(3,4),(4,8),(5,8),(6,7),(8,7)],9)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0,1,0] => [[[[.,.],[.,.]],.],[[[.,.],.],[.,.]]] => ([(0,6),(1,6),(2,7),(3,5),(4,8),(5,7),(6,4),(7,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]] => ([(0,8),(1,7),(2,4),(3,8),(4,9),(5,6),(6,3),(7,5),(8,9)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]] => ([(0,9),(1,9),(2,8),(3,8),(5,7),(6,5),(7,3),(8,4),(9,6)],10)
[1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]] => ([(0,9),(1,9),(2,8),(4,8),(5,4),(6,3),(7,6),(8,7),(9,5)],10)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]] => ([(0,7),(1,8),(2,8),(3,9),(5,6),(6,7),(7,9),(8,5),(9,4)],10)
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]] => ([(0,9),(1,8),(2,8),(4,5),(5,7),(6,4),(7,3),(8,9),(9,6)],10)
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]] => ([(0,7),(1,7),(2,8),(3,9),(5,6),(6,9),(7,8),(8,5),(9,4)],10)
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]] => ([(0,7),(1,7),(2,8),(3,9),(4,6),(6,5),(7,9),(8,4),(9,8)],10)
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,6),(2,9),(3,7),(4,8),(6,8),(7,9),(8,7),(9,5)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0] => [.,[[.,[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.]],.]] => ([(0,11),(1,11),(3,5),(4,3),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8),(11,10)],12)
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0] => [.,[[[.,[[.,[[.,[[.,.],[.,.]]],.]],.]],.],[.,.]]] => ([(0,11),(1,11),(2,10),(3,10),(5,7),(6,5),(7,9),(8,6),(9,3),(10,4),(11,8)],12)
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]]],.]] => ([(0,11),(1,11),(2,10),(4,10),(5,6),(6,4),(7,5),(8,3),(9,8),(10,9),(11,7)],12)
[1,0,1,1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0,1,0,0,1,0] => [.,[[[[.,[[.,[[.,.],[.,.]]],.]],.],[.,.]],[.,.]]] => ([(0,10),(1,11),(2,11),(3,9),(4,9),(6,8),(7,6),(8,4),(9,10),(10,5),(11,7)],12)
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0] => [.,[[.,[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.]],.]] => ([(0,11),(1,11),(2,10),(4,10),(5,8),(6,5),(7,4),(8,3),(9,6),(10,9),(11,7)],12)
[1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,0,1,0] => [.,[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],.],[.,.]]] => ([(0,10),(1,10),(2,11),(3,9),(4,11),(6,9),(7,6),(8,4),(9,8),(10,7),(11,5)],12)
[1,0,1,1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]]],.]] => ([(0,11),(1,11),(2,9),(3,10),(5,9),(6,4),(7,5),(8,6),(9,10),(10,8),(11,7)],12)
[1,0,1,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[.,[[.,.],[.,.]]],.],[.,.]],[.,.]],[.,.]]] => ([(0,9),(1,10),(2,10),(3,11),(4,8),(6,7),(7,8),(8,9),(9,11),(10,6),(11,5)],12)
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0] => [.,[[.,[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.]],.]] => ([(0,11),(1,10),(2,10),(4,5),(5,7),(6,4),(7,9),(8,6),(9,3),(10,11),(11,8)],12)
[1,0,1,1,1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0] => [.,[[[.,[[.,[[[.,.],[.,.]],[.,.]]],.]],.],[.,.]]] => ([(0,10),(1,10),(2,11),(3,9),(4,9),(6,8),(7,6),(8,4),(9,5),(10,11),(11,7)],12)
[1,0,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]]],.]] => ([(0,9),(1,9),(2,10),(3,11),(5,10),(6,4),(7,5),(8,6),(9,11),(10,8),(11,7)],12)
[1,0,1,1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => [.,[[[[.,[[[.,.],[.,.]],[.,.]]],.],[.,.]],[.,.]]] => ([(0,10),(1,11),(2,8),(3,8),(4,9),(6,7),(7,9),(8,10),(9,11),(10,6),(11,5)],12)
[1,0,1,1,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [.,[[.,[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.]],.]] => ([(0,10),(1,10),(2,11),(3,9),(5,6),(6,8),(7,5),(8,4),(9,11),(10,9),(11,7)],12)
[1,0,1,1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => [.,[[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],.],[.,.]]] => ([(0,11),(1,9),(2,10),(3,8),(4,8),(6,7),(7,11),(8,9),(9,10),(10,6),(11,5)],12)
[1,0,1,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],.]] => ([(0,8),(1,8),(2,10),(3,11),(4,9),(5,7),(7,6),(8,11),(9,5),(10,9),(11,10)],12)
[1,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]] => ([(0,7),(1,7),(2,11),(3,9),(4,10),(5,8),(7,10),(8,11),(9,8),(10,9),(11,6)],12)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] => ([(0,8),(1,9),(2,4),(3,5),(4,9),(5,6),(6,7),(7,8),(9,7)],10)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] => ([(0,8),(1,7),(2,4),(3,5),(4,9),(5,6),(6,9),(7,8),(9,7)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] => ([(0,8),(1,9),(2,4),(3,7),(4,6),(5,9),(6,5),(7,8),(9,7)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]] => ([(0,7),(1,6),(2,4),(3,7),(4,8),(5,3),(6,5),(7,8)],9)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] => ([(0,8),(1,9),(2,7),(3,4),(4,9),(5,6),(6,7),(7,8),(9,5)],10)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] => ([(0,8),(1,9),(2,7),(3,4),(4,9),(5,6),(6,7),(8,5),(9,8)],10)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[[.,.],[.,.]],[[[.,.],[[.,.],.]],.]] => ([(0,8),(1,6),(2,6),(3,4),(4,8),(5,7),(6,7),(8,5)],9)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[.,[.,[.,[[.,.],[.,.]]]]],[.,[.,.]]] => ([(0,8),(1,8),(2,4),(3,7),(4,7),(5,6),(6,3),(8,5)],9)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]] => ([(0,8),(1,6),(2,6),(3,7),(4,7),(6,8),(7,9),(8,9),(9,5)],10)
[1,1,0,1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0,0] => [[.,[[[.,[[.,.],.]],[[.,[.,.]],.]],.]],.] => ([(0,8),(1,7),(3,9),(4,9),(5,2),(6,5),(7,3),(8,4),(9,6)],10)
[1,1,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]] => ([(0,7),(1,7),(2,9),(3,10),(4,8),(5,6),(6,11),(7,10),(8,11),(9,8),(10,9)],12)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => [[[[.,[[.,[.,.]],.]],.],[[.,[[.,[.,.]],.]],.]],.] => ([(0,10),(1,9),(2,11),(3,11),(5,7),(6,8),(7,2),(8,3),(9,5),(10,6),(11,4)],12)
[1,1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0,1,0,0] => [[[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],[.,.]],.] => ([(0,11),(1,10),(2,9),(3,11),(4,10),(6,7),(7,4),(8,6),(9,3),(10,5),(11,8)],12)
[1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0,0] => [[.,[[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.]],.] => ([(0,10),(1,11),(2,7),(4,11),(5,10),(6,3),(7,5),(8,6),(9,4),(10,9),(11,8)],12)
[1,1,0,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[.,[[.,[[[.,[[.,.],.]],[.,.]],.]],.]],.] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0,0] => [[[.,[[.,.],.]],[.,[[[.,.],[.,.]],.]]],.] => ([(0,8),(1,8),(2,6),(3,9),(5,9),(6,5),(7,3),(8,7),(9,4)],10)
[1,1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,[[.,.],.]],[.,.]],.]],[.,.]],.] => ([(0,9),(1,8),(2,6),(3,9),(5,8),(6,5),(7,3),(8,7),(9,4)],10)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,.],[.,[[[.,.],[[.,.],.]],.]]],.]] => ([(0,8),(1,9),(2,5),(4,8),(5,9),(6,4),(7,3),(8,7),(9,6)],10)
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.] => ([(0,11),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,10),(9,7),(10,1),(11,9)],12)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]] => ([(0,7),(1,7),(2,6),(3,6),(4,5),(6,8),(7,8),(8,4)],9)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [[[.,.],[[.,[.,[.,[.,.]]]],.]],[.,.]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0] => [[[.,[[.,.],[[.,.],[.,.]]]],[.,.]],[.,.]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,9),(6,8),(8,5),(9,7)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => ([(0,7),(1,7),(2,11),(3,9),(4,10),(5,8),(7,10),(8,11),(9,8),(10,9),(11,6)],12)
[1,1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,.],[.,[[[.,.],[.,.]],.]]],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,9),(5,6),(6,7),(7,9),(8,5),(9,4)],10)
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [[[.,.],[[.,[[.,[[.,[.,.]],.]],.]],.]],.] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => [[[.,.],[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],.]],.] => ([(0,11),(1,8),(2,9),(3,10),(4,10),(6,11),(7,3),(8,4),(9,7),(10,6),(11,5)],12)
[1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]],.] => ([(0,11),(1,10),(2,11),(4,5),(5,7),(6,4),(7,9),(8,6),(9,2),(10,8),(11,3)],12)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],[[.,.],.]] => ([(0,8),(1,5),(2,6),(3,8),(4,7),(5,7),(6,3),(8,4)],9)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0,1,0] => [[[[[.,.],.],[.,.]],.],[[.,.],[.,.]]] => ([(0,8),(1,6),(2,6),(3,4),(4,8),(5,7),(6,7),(8,5)],9)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0,1,0] => [[[[.,[.,.]],.],[.,.]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,7),(3,4),(4,5),(5,7),(6,8),(7,8)],9)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]] => ([(0,8),(1,8),(2,6),(3,7),(4,5),(5,3),(6,4),(8,7)],9)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[[[.,.],.],[.,.]],[[.,.],[[.,.],.]]] => ([(0,8),(1,7),(2,4),(3,5),(4,7),(5,8),(7,6),(8,6)],9)
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [[[[.,[[.,.],[.,.]]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,8),(2,8),(3,9),(4,6),(5,9),(6,7),(8,5),(9,6)],10)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.] => ([(0,8),(1,9),(2,7),(3,4),(4,9),(5,6),(7,8),(8,5),(9,7)],10)
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]],.] => ([(0,9),(1,10),(2,11),(3,8),(4,5),(5,11),(6,7),(8,9),(9,10),(10,6),(11,8)],12)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]] => ([(0,9),(1,7),(2,8),(3,4),(4,9),(6,8),(7,5),(8,7),(9,6)],10)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]] => ([(0,9),(1,7),(2,6),(4,8),(5,8),(6,4),(7,5),(8,9),(9,3)],10)
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => ([(0,8),(1,9),(2,7),(3,9),(5,8),(6,3),(7,6),(8,4),(9,5)],10)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => ([(0,9),(1,7),(2,8),(3,6),(5,9),(6,8),(7,5),(8,7),(9,4)],10)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => ([(0,8),(1,6),(2,7),(4,9),(5,8),(6,4),(7,5),(8,9),(9,3)],10)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => ([(0,9),(1,6),(2,7),(3,8),(5,8),(6,9),(7,3),(8,4),(9,5)],10)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => ([(0,8),(1,7),(2,9),(3,9),(5,6),(6,3),(7,5),(8,2),(9,4)],10)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]] => ([(0,9),(1,6),(2,7),(3,8),(5,8),(6,9),(7,3),(8,4),(9,5)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]] => ([(0,8),(1,11),(2,9),(3,10),(4,6),(6,7),(7,8),(8,10),(9,11),(10,9),(11,5)],12)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[.,.],[[[.,[.,.]],[.,.]],.]]]]] => ([(0,11),(1,9),(2,10),(3,8),(4,6),(6,11),(7,10),(8,9),(9,5),(10,8),(11,7)],12)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[.,.]],.],[[.,[.,.]],.]]]]] => ([(0,10),(1,11),(2,8),(3,7),(5,9),(6,9),(7,5),(8,6),(9,10),(10,11),(11,4)],12)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[.,[[.,[.,.]],.]],[.,.]],.]]]] => ([(0,9),(1,10),(2,11),(3,8),(4,10),(6,9),(7,4),(8,7),(9,11),(10,6),(11,5)],12)
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[.,.],[[[[.,[.,.]],[.,.]],[.,.]],.]]]] => ([(0,10),(1,11),(2,8),(3,9),(4,5),(5,11),(7,10),(8,6),(9,7),(10,8),(11,9)],12)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[.,.],[[.,[.,.]],.]]]]] => ([(0,10),(1,11),(2,7),(3,8),(5,10),(6,9),(7,5),(8,6),(9,11),(10,9),(11,4)],12)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,.],[[[.,[.,.]],.],[[[.,[.,.]],[.,.]],.]]]] => ([(0,10),(1,11),(2,5),(3,8),(4,9),(5,10),(7,9),(8,4),(9,11),(10,7),(11,6)],12)
[1,0,1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[.,[[.,[.,.]],.]],.],[[.,[.,.]],.]]]] => ([(0,11),(1,9),(2,8),(3,10),(4,10),(6,7),(7,4),(8,6),(9,3),(10,11),(11,5)],12)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[.,.]],.],[[.,[.,.]],.]]]] => ([(0,10),(1,11),(2,5),(3,8),(4,9),(5,10),(7,9),(8,4),(9,11),(10,7),(11,6)],12)
[1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]] => ([(0,9),(1,10),(2,11),(3,4),(4,9),(5,10),(7,11),(8,5),(9,8),(10,7),(11,6)],12)
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,.],[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]] => ([(0,10),(1,11),(2,5),(3,8),(4,9),(5,9),(7,10),(8,4),(9,11),(10,6),(11,7)],12)
[1,0,1,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]] => ([(0,9),(1,10),(2,11),(3,8),(4,9),(6,10),(7,4),(8,7),(9,11),(10,5),(11,6)],12)
[1,0,1,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [.,[[.,.],[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]] => ([(0,11),(1,9),(2,10),(3,8),(4,7),(6,11),(7,10),(8,9),(9,6),(10,8),(11,5)],12)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[.,.],[[.,[.,.]],.]]]]] => ([(0,10),(1,9),(2,7),(3,8),(5,11),(6,9),(7,5),(8,6),(9,10),(10,11),(11,4)],12)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],[[[.,[.,.]],[.,.]],.]]]] => ([(0,11),(1,9),(2,5),(3,8),(4,9),(5,11),(6,10),(8,6),(9,10),(10,7),(11,4)],12)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[.,.]],.],[[.,[.,.]],.]]]] => ([(0,9),(1,8),(2,7),(4,11),(5,10),(6,10),(7,4),(8,5),(9,6),(10,11),(11,3)],12)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[.,[[.,[.,.]],.]],[.,.]],.]]] => ([(0,11),(1,8),(2,9),(3,11),(4,10),(6,10),(7,3),(8,4),(9,7),(10,5),(11,6)],12)
[1,0,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[[[.,[.,.]],[.,.]],[.,.]],.]]] => ([(0,11),(1,9),(2,4),(3,8),(4,9),(5,10),(6,10),(8,6),(9,11),(10,7),(11,5)],12)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[.,.],[[.,[.,.]],.]]]] => ([(0,10),(1,8),(2,9),(3,11),(4,10),(6,7),(7,3),(8,6),(9,4),(10,11),(11,5)],12)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],.],[[[.,[.,.]],[.,.]],.]]] => ([(0,11),(1,9),(2,6),(3,10),(5,10),(6,11),(7,8),(8,3),(9,7),(10,4),(11,5)],12)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[.,.],[[.,[.,.]],.]]]] => ([(0,11),(1,9),(2,5),(3,8),(4,9),(5,11),(6,10),(8,4),(9,10),(10,7),(11,6)],12)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[[.,[.,.]],[.,.]],.],[[[.,[.,.]],[.,.]],.]]] => ([(0,11),(1,10),(2,5),(3,6),(5,10),(6,11),(7,9),(8,9),(9,4),(10,7),(11,8)],12)
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],.],[[.,[.,.]],.]]] => ([(0,10),(1,9),(2,6),(3,11),(5,11),(6,10),(7,5),(8,7),(9,3),(10,8),(11,4)],12)
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[.,.]],[[.,[.,.]],.]],.],[[.,[.,.]],.]]] => ([(0,7),(1,8),(2,9),(3,10),(4,11),(6,10),(7,11),(8,3),(9,4),(10,5),(11,6)],12)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[.,[[.,[.,.]],.]],[.,.]],.],[[.,[.,.]],.]]] => ([(0,11),(1,8),(2,9),(3,11),(4,10),(6,10),(7,3),(8,4),(9,7),(10,5),(11,6)],12)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => [.,[[[[[.,[.,.]],[.,.]],[.,.]],.],[[.,[.,.]],.]]] => ([(0,11),(1,9),(2,4),(3,8),(4,9),(5,10),(6,10),(8,6),(9,11),(10,7),(11,5)],12)
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.
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 poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
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