Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
Images
[1,0] => [1] => [.,.] => ([],1)
[1,0,1,0] => [1,2] => [.,[.,.]] => ([(0,1)],2)
[1,1,0,0] => [2,1] => [[.,.],.] => ([(0,1)],2)
[1,0,1,0,1,0] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3)
[1,0,1,1,0,0] => [1,3,2] => [.,[[.,.],.]] => ([(0,2),(2,1)],3)
[1,1,0,0,1,0] => [2,1,3] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[1,1,0,1,0,0] => [2,3,1] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[1,1,1,0,0,0] => [3,2,1] => [[[.,.],.],.] => ([(0,2),(2,1)],3)
[1,0,1,0,1,0,1,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,1,0,0] => [1,2,4,3] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,1,0,0,1,0] => [1,3,2,4] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4)
[1,0,1,1,0,1,0,0] => [1,3,4,2] => [.,[[.,.],[.,.]]] => ([(0,3),(1,3),(3,2)],4)
[1,0,1,1,1,0,0,0] => [1,4,3,2] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4)
[1,1,0,0,1,0,1,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,1,0,0] => [2,1,4,3] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0,1,0] => [2,3,1,4] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,1,0,0] => [2,3,4,1] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,1,0,0,0] => [2,4,3,1] => [[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,0,1,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,1,0,0] => [3,2,4,1] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,1,0,0,0] => [3,4,2,1] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,1,0,0,0,0] => [4,3,2,1] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4)
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(4,2)],5)
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,1,0,1,0,0,0] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]] => ([(0,4),(1,2),(2,4),(4,3)],5)
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,1,1,0,1,0,0,0] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]] => ([(0,4),(1,3),(2,3),(3,4)],5)
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,1,0,0,0,1,0] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,1,0,0,1,0,0] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,1,0,1,0,0,0] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,0,1,1,0,0,0,0] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5)
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,1,0,0,1,0,0,0] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,1,0,1,0,0,0,0] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5)
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5)
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6)
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6)
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6)
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6)
>>> Load all 1980 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6)
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,0,1,0,1,0] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,0,1,1,0,0] => [3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,1,0,0,1,0] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,1,0,1,0,0] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,1,0,0,0,1,0] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,1,0,0,1,0,0] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,0,1,1,0,0,0,0,1,0] => [3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,1,0,0,0,1,0,0] => [3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,1,0,1,1,1,0,0,0,0,0] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,1,0,0,0,1,0] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,1,0,0,0,0,1,0] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,1,0,1,0,0,0,0] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,0,1,1,0,0,0,0,0] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,0,0,0,1,0,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,0,0,1,0,0,0,0] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,0,1,0,0,0,0,0] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => ([(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] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,2,3,4,5,7,6] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(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] => [1,2,3,4,6,5,7] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(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] => [1,2,3,4,6,7,5] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,7,6,5] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(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] => [1,2,3,5,4,6,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [1,2,3,5,4,7,6] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(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] => [1,2,3,5,6,4,7] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [1,2,3,5,6,7,4] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,5,7,6,4] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,6,5,4,7] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(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] => [1,2,3,6,5,7,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,6,7,5,4] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,7,6,5,4] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(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] => [1,2,4,3,5,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(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] => [1,2,4,3,5,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(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] => [1,2,4,3,6,5,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(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] => [1,2,4,3,6,7,5] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,4,3,7,6,5] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(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] => [1,2,4,5,3,6,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,4,5,3,7,6] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,3,7] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(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] => [1,2,4,5,6,7,3] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,4,5,7,6,3] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,4,6,5,3,7] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,4,6,5,7,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,4,6,7,5,3] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,4,7,6,5,3] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,5,4,3,6,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(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] => [1,2,5,4,3,7,6] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(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] => [1,2,5,4,6,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,5,4,6,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,5,4,7,6,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,5,6,4,3,7] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,5,6,4,7,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,5,6,7,4,3] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,5,7,6,4,3] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,6,5,4,3,7] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(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] => [1,2,6,5,4,7,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,6,5,7,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,6,7,5,4,3] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,7,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(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] => [1,3,2,4,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(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] => [1,3,2,4,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(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] => [1,3,2,4,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(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] => [1,3,2,4,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,3,2,4,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(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] => [1,3,2,5,4,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(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] => [1,3,2,5,4,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(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] => [1,3,2,5,6,4,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(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] => [1,3,2,5,6,7,4] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,3,2,5,7,6,4] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,3,2,6,5,4,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(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] => [1,3,2,6,5,7,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,3,2,6,7,5,4] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,3,2,7,6,5,4] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(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] => [1,3,4,2,5,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [1,3,4,2,5,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,2,6,5,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,2,6,7,5] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,2,7,6,5] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,2,6,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,2,7,6] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,2,7] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(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] => [1,3,4,5,6,7,2] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,7,6,2] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,6,5,2,7] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,6,5,7,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,6,7,5,2] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,7,6,5,2] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,3,5,4,2,6,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [1,3,5,4,2,7,6] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,3,5,4,6,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,3,5,4,6,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,3,5,4,7,6,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,3,5,6,4,2,7] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [1,3,5,6,4,7,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,3,5,6,7,4,2] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,3,5,7,6,4,2] => [.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [1,3,6,5,4,2,7] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,3,6,5,4,7,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [1,3,6,5,7,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,3,6,7,5,4,2] => [.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,3,7,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(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] => [1,4,3,2,5,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(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] => [1,4,3,2,6,5,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(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] => [1,4,3,2,6,7,5] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,4,3,2,7,6,5] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(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] => [1,4,3,5,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [1,4,3,5,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,4,3,5,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,3,5,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,4,3,6,5,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,4,3,6,5,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,3,6,7,5,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,3,7,6,5,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,4,5,3,2,6,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(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] => [1,4,5,3,2,7,6] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(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] => [1,4,5,3,6,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,4,5,3,6,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,5,3,7,6,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,3,2,7] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,3,7,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,3,2] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,4,5,7,6,3,2] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,4,6,5,3,2,7] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,4,6,5,3,7,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,4,6,5,7,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [1,4,6,7,5,3,2] => [.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,4,7,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,5,4,3,2,6,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(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] => [1,5,4,3,2,7,6] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(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] => [1,5,4,3,6,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,4,3,6,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,4,3,7,6,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [1,5,4,6,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,5,4,6,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,5,4,6,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,5,4,7,6,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,5,6,4,3,2,7] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [1,5,6,4,3,7,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,5,6,4,7,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,5,6,7,4,3,2] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,5,7,6,4,3,2] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,6,5,4,3,2,7] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(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] => [1,6,5,4,3,7,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,6,5,4,7,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,6,5,7,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,6,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,7,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(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] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(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] => [2,1,3,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(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] => [2,1,3,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(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] => [2,1,3,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(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] => [2,1,3,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(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] => [2,1,3,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(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] => [2,1,3,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(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] => [2,1,3,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [2,1,3,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(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] => [2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(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] => [2,1,4,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(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] => [2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(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] => [2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(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] => [2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(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] => [2,1,4,5,3,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,3,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(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] => [2,1,4,5,6,7,3] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,1,4,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(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] => [2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(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] => [2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,1,5,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,1,5,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,1,5,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(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] => [2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,1,6,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,1,6,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,1,7,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(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] => [2,3,1,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,1,4,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,1,4,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,1,4,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,1,5,4,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,1,5,4,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,1,5,6,4,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,1,5,6,7,4] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,1,5,7,6,4] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,1,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,1,5,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,1,6,5,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,1,6,7,5] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,1,7,6,5] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,1,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,1,7,6] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,1,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(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] => [2,3,4,5,6,7,1] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,7,6,1] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,6,5,1,7] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,6,5,7,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,6,7,5,1] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,7,6,5,1] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,5,4,1,6,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [2,3,5,4,1,7,6] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,5,4,6,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,5,4,6,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,4,7,6,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,5,6,4,1,7] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,5,6,4,7,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,6,7,4,1] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,7,6,4,1] => [[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,6,5,7,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,5,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,7,6,5,4,1] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,4,3,1,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,4,3,1,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [2,4,3,1,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,4,3,1,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,4,3,5,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [2,4,3,5,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,4,3,5,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [2,4,3,5,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [2,4,3,6,5,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,4,3,6,5,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,4,3,6,7,5,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,4,3,7,6,5,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,4,5,3,1,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,4,5,3,1,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,4,5,3,6,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,4,5,3,6,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,4,5,3,7,6,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,3,1,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,3,7,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,3,1] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,4,5,7,6,3,1] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,4,6,5,3,1,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,4,6,5,3,7,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,4,6,5,7,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,4,6,7,5,3,1] => [[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,4,7,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,5,4,3,1,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,5,4,3,1,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [2,5,4,3,6,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,5,4,3,6,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [2,5,4,3,7,6,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,5,4,6,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [2,5,4,6,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [2,5,4,6,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,5,4,7,6,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,5,6,4,3,1,7] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,5,6,4,3,7,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [2,5,6,4,7,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,5,6,7,4,3,1] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,5,7,6,4,3,1] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,6,5,4,3,1,7] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,6,5,4,3,7,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,6,5,4,7,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,6,5,7,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,6,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,7,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [3,2,1,4,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(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] => [3,2,1,4,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(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] => [3,2,1,4,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [3,2,1,4,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(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] => [3,2,1,5,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(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] => [3,2,1,5,4,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(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] => [3,2,1,5,6,4,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(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] => [3,2,1,5,6,7,4] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [3,2,1,5,7,6,4] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [3,2,1,6,5,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(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] => [3,2,1,6,5,7,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [3,2,1,6,7,5,4] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,2,1,7,6,5,4] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(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] => [3,2,4,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [3,2,4,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [3,2,4,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [3,2,4,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [3,2,4,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [3,2,4,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [3,2,4,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [3,2,4,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [3,2,4,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,2,4,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [3,2,5,4,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(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] => [3,2,5,4,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(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] => [3,2,5,4,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [3,2,5,4,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [3,2,5,4,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [3,2,5,6,4,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [3,2,5,6,4,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [3,2,5,6,7,4,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,2,5,7,6,4,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [3,2,6,5,4,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [3,2,6,5,4,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [3,2,6,5,7,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,6,7,5,4,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,2,7,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,2,1,5,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,2,1,6,5,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [3,4,2,1,6,7,5] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,2,1,7,6,5] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,2,5,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,2,5,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,2,5,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [3,4,2,5,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,2,6,5,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,2,6,5,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,2,6,7,5,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,4,2,7,6,5,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,2,1,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [3,4,5,2,1,7,6] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(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] => [3,4,5,2,6,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,2,6,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,2,7,6,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,2,1,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,2,7,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,2,1] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,7,6,2,1] => [[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [3,4,6,5,2,1,7] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,6,5,2,7,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,6,5,7,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,6,7,5,2,1] => [[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,7,6,5,2,1] => [[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [3,5,4,2,1,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [3,5,4,2,1,7,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [3,5,4,2,6,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [3,5,4,2,6,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [3,5,4,2,7,6,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [3,5,4,6,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [3,5,4,6,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [3,5,4,6,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,5,4,7,6,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,5,6,4,2,1,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [3,5,6,4,2,7,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [3,5,6,4,7,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,5,6,7,4,2,1] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,5,7,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,6,5,4,2,1,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [3,6,5,4,2,7,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [3,6,5,4,7,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,6,5,7,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,6,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,7,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(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] => [4,3,2,1,5,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(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] => [4,3,2,1,6,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(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] => [4,3,2,1,6,7,5] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,3,2,1,7,6,5] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(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] => [4,3,2,5,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [4,3,2,5,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,3,2,5,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [4,3,2,6,5,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [4,3,2,6,5,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,2,6,7,5,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,3,2,7,6,5,1] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [4,3,5,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [4,3,5,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [4,3,5,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,3,5,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [4,3,5,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,3,5,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [4,3,6,5,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [4,3,6,5,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,3,6,5,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,6,7,5,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,3,7,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [4,5,3,2,1,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [4,5,3,2,1,7,6] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [4,5,3,2,6,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [4,5,3,2,6,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,5,3,2,7,6,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [4,5,3,6,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [4,5,3,6,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,3,7,6,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,3,2,1,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,3,2,7,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,7,6,3,2,1] => [[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [4,6,5,3,2,1,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [4,6,5,3,2,7,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,6,5,3,7,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,6,5,7,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,6,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [4,7,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(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] => [5,4,3,2,1,7,6] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(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] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,4,3,2,7,6,1] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [5,4,3,7,6,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [5,4,6,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [5,4,7,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [5,6,4,3,2,1,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,6,4,3,2,7,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [5,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(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] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => ([(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] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [1,2,3,4,5,6,8,7] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(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] => [1,2,3,4,5,7,6,8] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(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] => [1,2,3,4,5,7,8,6] => [.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,7),(1,7),(3,5),(4,3),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,8,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(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] => [1,2,3,4,6,5,7,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(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] => [1,2,3,4,6,5,8,7] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => ([(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] => [1,2,3,4,6,7,5,8] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(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] => [1,2,3,4,6,7,8,5] => [.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,6,8,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,3,4,7,6,5,8] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(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] => [1,2,3,4,7,6,8,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,7,8,6,5] => [.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] => ([(0,7),(1,3),(3,7),(4,5),(5,2),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,8,7,6,5] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(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] => [1,2,3,5,4,6,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(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] => [1,2,3,5,4,6,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => ([(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] => [1,2,3,5,4,7,6,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(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] => [1,2,3,5,4,7,8,6] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [1,2,3,5,4,8,7,6] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => ([(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] => [1,2,3,5,6,4,7,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [1,2,3,5,6,4,8,7] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,5,6,7,4,8] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(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] => [1,2,3,5,6,7,8,4] => [.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [1,2,3,5,6,8,7,4] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [1,2,3,5,7,6,4,8] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [1,2,3,5,7,6,8,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,5,7,8,6,4] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(5,4),(6,7),(7,3)],8)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,5,8,7,6,4] => [.,[.,[.,[[.,.],[[[.,.],.],.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [1,2,3,6,5,4,7,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(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] => [1,2,3,6,5,4,8,7] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => ([(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] => [1,2,3,6,5,7,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [1,2,3,6,5,7,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [1,2,3,6,5,8,7,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [1,2,3,6,7,5,4,8] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [1,2,3,6,7,5,8,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,2,3,6,7,8,5,4] => [.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [1,2,3,6,8,7,5,4] => [.,[.,[.,[[[.,.],.],[[.,.],.]]]]] => ([(0,4),(1,3),(3,7),(4,7),(5,2),(6,5),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [1,2,3,7,6,5,4,8] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(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] => [1,2,3,7,6,5,8,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [1,2,3,7,6,8,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [1,2,3,7,8,6,5,4] => [.,[.,[.,[[[[.,.],.],.],[.,.]]]]] => ([(0,7),(1,5),(3,7),(4,2),(5,3),(6,4),(7,6)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,8,7,6,5,4] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(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] => [1,2,4,3,5,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,2,4,3,5,6,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => ([(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] => [1,2,4,3,5,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(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] => [1,2,4,3,5,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [1,2,4,3,5,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => ([(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] => [1,2,4,3,6,5,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(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] => [1,2,4,3,6,5,8,7] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(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] => [1,2,4,3,6,7,5,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(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] => [1,2,4,3,6,7,8,5] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,2,4,3,6,8,7,5] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(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] => [1,2,4,3,7,6,8,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [1,2,4,3,7,8,6,5] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [1,2,4,3,8,7,6,5] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => ([(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] => [1,2,4,5,3,6,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,2,4,5,3,7,6,8] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [1,2,4,5,3,7,8,6] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [1,2,4,5,3,8,7,6] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [1,2,4,5,6,3,7,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [1,2,4,5,6,3,8,7] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [1,2,4,5,6,7,3,8] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,2,4,5,6,7,8,3] => [.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,2,4,5,6,8,7,3] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [1,2,4,5,7,8,6,3] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(6,4),(7,3)],8)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,2,4,5,8,7,6,3] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [1,2,4,6,5,3,7,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,2,4,6,5,7,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [1,2,4,6,5,8,7,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [1,2,4,6,7,5,3,8] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [1,2,4,6,7,8,5,3] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [1,2,4,6,8,7,5,3] => [.,[.,[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,2,4,7,6,5,8,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,2,4,7,8,6,5,3] => [.,[.,[[.,.],[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(6,4),(7,6)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,4,8,7,6,5,3] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [1,2,5,4,3,6,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(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] => [1,2,5,4,3,6,8,7] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [1,2,5,4,3,7,8,6] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [1,2,5,4,3,8,7,6] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [1,2,5,4,6,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [1,2,5,4,6,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [1,2,5,4,6,8,7,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [1,2,5,4,7,6,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [1,2,5,4,7,8,6,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [1,2,5,4,8,7,6,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [1,2,5,6,4,3,7,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(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] => [1,2,5,6,4,7,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [1,2,5,6,4,7,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [1,2,5,6,7,4,3,8] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [1,2,5,6,7,4,8,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [1,2,5,6,7,8,4,3] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [1,2,5,6,8,7,4,3] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [1,2,5,7,6,4,3,8] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [1,2,5,7,6,4,8,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [1,2,5,7,6,8,4,3] => [.,[.,[[[.,.],.],[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(6,7),(7,4)],8)
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [1,2,5,8,7,6,4,3] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [1,2,6,5,4,3,7,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [1,2,6,5,4,7,8,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [1,2,6,5,4,8,7,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [1,2,6,5,7,8,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,6,5,8,7,4,3] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [1,2,6,7,5,4,3,8] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [1,2,6,7,8,5,4,3] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(3,7),(4,7),(5,2),(6,3),(7,5)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [1,2,7,6,5,4,3,8] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(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] => [1,2,7,6,5,4,8,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,2,7,6,5,8,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [1,2,7,6,8,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [1,2,7,8,6,5,4,3] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,8,7,6,5,4,3] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => ([(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] => [1,3,2,4,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,3,2,4,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(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] => [1,3,2,4,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(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] => [1,3,2,4,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [1,3,2,4,5,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => ([(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] => [1,3,2,4,6,5,7,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [1,3,2,4,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(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] => [1,3,2,4,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [1,3,2,4,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [1,3,2,4,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [1,3,2,4,7,6,5,8] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(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] => [1,3,2,4,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [1,3,2,4,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => ([(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] => [1,3,2,5,4,6,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(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] => [1,3,2,5,4,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(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] => [1,3,2,5,4,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,5,4,8,7,6] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(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] => [1,3,2,5,6,4,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [1,3,2,5,6,4,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [1,3,2,5,6,7,4,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(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] => [1,3,2,5,6,7,8,4] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,3,2,5,6,8,7,4] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [1,3,2,5,7,6,4,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [1,3,2,5,7,8,6,4] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,3,2,5,8,7,6,4] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [1,3,2,6,5,4,7,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(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] => [1,3,2,6,5,4,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(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] => [1,3,2,6,5,7,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [1,3,2,6,5,7,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [1,3,2,6,5,8,7,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [1,3,2,6,7,5,4,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [1,3,2,6,7,5,8,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [1,3,2,6,7,8,5,4] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [1,3,2,6,8,7,5,4] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [1,3,2,7,6,5,4,8] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(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] => [1,3,2,7,6,5,8,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,3,2,7,6,8,5,4] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [1,3,2,8,7,6,5,4] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => ([(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] => [1,3,4,2,5,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [1,3,4,2,5,6,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [1,3,4,2,5,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [1,3,4,2,5,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [1,3,4,2,6,5,8,7] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [1,3,4,2,6,7,5,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [1,3,4,2,6,7,8,5] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,3,4,2,6,8,7,5] => [.,[[.,.],[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [1,3,4,2,7,6,8,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [1,3,4,2,7,8,6,5] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [1,3,4,2,8,7,6,5] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [1,3,4,5,2,7,6,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [1,3,4,5,2,7,8,6] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [1,3,4,5,2,8,7,6] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,2,7,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,2,8,7] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,2,8] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,3,4,5,6,7,8,2] => [.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,8,7,2] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [1,3,4,5,7,6,2,8] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [1,3,4,5,7,6,8,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [1,3,4,5,7,8,6,2] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,7),(4,5),(5,7),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,3,4,5,8,7,6,2] => [.,[[.,.],[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,3,4,6,5,7,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [1,3,4,6,5,7,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [1,3,4,6,7,5,2,8] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [1,3,4,6,7,5,8,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [1,3,4,6,7,8,5,2] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,3,4,7,6,5,8,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [1,3,4,7,6,8,5,2] => [.,[[.,.],[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,7),(2,3),(3,7),(5,6),(6,4),(7,5)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,3,4,8,7,6,5,2] => [.,[[.,.],[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [1,3,5,4,2,6,8,7] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [1,3,5,4,2,7,6,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [1,3,5,4,2,7,8,6] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [1,3,5,4,7,6,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [1,3,5,4,7,6,8,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [1,3,5,4,8,7,6,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [1,3,5,6,4,2,7,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [1,3,5,6,4,7,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [1,3,5,6,7,4,2,8] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [1,3,5,6,7,4,8,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [1,3,5,6,7,8,4,2] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [1,3,5,6,8,7,4,2] => [.,[[.,.],[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,3,5,7,6,4,2,8] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [1,3,5,7,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(5,6),(6,7),(7,4)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [1,3,5,8,7,6,4,2] => [.,[[.,.],[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [1,3,6,5,4,2,8,7] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,3,6,5,4,7,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [1,3,6,5,4,8,7,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [1,3,6,5,7,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [1,3,6,5,7,4,8,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [1,3,6,5,7,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [1,3,6,7,5,4,2,8] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [1,3,6,7,5,8,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,3,6,7,8,5,4,2] => [.,[[.,.],[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,3,6,8,7,5,4,2] => [.,[[.,.],[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(6,5),(7,6)],8)
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,3,7,8,6,5,4,2] => [.,[[.,.],[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,4),(4,5),(5,6),(6,7),(7,3)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,3,8,7,6,5,4,2] => [.,[[.,.],[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,4,3,2,5,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(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] => [1,4,3,2,5,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(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] => [1,4,3,2,5,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(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] => [1,4,3,2,5,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [1,4,3,2,5,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [1,4,3,2,6,7,5,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(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] => [1,4,3,2,6,7,8,5] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [1,4,3,2,6,8,7,5] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [1,4,3,2,7,6,5,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(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] => [1,4,3,2,7,6,8,5] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [1,4,3,2,8,7,6,5] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => ([(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] => [1,4,3,5,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,4,3,5,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [1,4,3,5,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,4,3,5,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [1,4,3,5,7,6,2,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [1,4,3,5,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,4,3,5,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [1,4,3,6,5,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(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] => [1,4,3,6,5,7,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [1,4,3,6,5,7,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [1,4,3,6,7,8,5,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [1,4,3,6,8,7,5,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,4,3,7,6,8,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [1,4,3,7,8,6,5,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [1,4,3,8,7,6,5,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [1,4,5,3,2,6,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [1,4,5,3,2,6,8,7] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [1,4,5,3,2,7,6,8] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [1,4,5,3,2,7,8,6] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [1,4,5,3,2,8,7,6] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,4,5,3,6,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [1,4,5,3,6,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [1,4,5,3,6,7,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [1,4,5,3,6,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [1,4,5,3,7,8,6,2] => [.,[[[.,.],.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(5,7),(6,5),(7,4)],8)
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [1,4,5,3,8,7,6,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [1,4,5,6,3,2,7,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(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] => [1,4,5,6,3,7,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [1,4,5,6,3,8,7,2] => [.,[[[.,.],.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [1,4,5,6,7,3,2,8] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [1,4,5,6,7,3,8,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,3,2] => [.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [1,4,5,8,7,6,3,2] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [1,4,6,5,3,2,7,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,4,6,5,3,8,7,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,4,6,5,7,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [1,4,6,5,7,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [1,4,6,5,8,7,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,4,6,7,5,3,2,8] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [1,4,6,7,5,3,8,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,4,6,7,5,8,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [1,4,6,7,8,5,3,2] => [.,[[[.,.],.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [1,4,6,8,7,5,3,2] => [.,[[[.,.],.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,4,7,6,5,3,2,8] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [1,4,7,6,5,8,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [1,4,7,8,6,5,3,2] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,5),(3,7),(5,6),(6,7),(7,4)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,4,8,7,6,5,3,2] => [.,[[[.,.],.],[[[[.,.],.],.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [1,5,4,3,2,6,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(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] => [1,5,4,3,2,7,6,8] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(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] => [1,5,4,3,2,7,8,6] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [1,5,4,3,2,8,7,6] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => ([(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] => [1,5,4,3,6,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,5,4,3,6,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,5,4,3,6,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,5,4,3,6,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [1,5,4,3,8,7,6,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [1,5,4,6,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [1,5,4,6,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [1,5,4,6,3,7,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [1,5,4,6,3,7,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [1,5,4,6,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [1,5,4,6,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [1,5,4,6,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [1,5,4,7,8,6,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [1,5,6,4,3,2,7,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [1,5,6,4,3,2,8,7] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [1,5,6,4,3,8,7,2] => [.,[[[[.,.],.],.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [1,5,6,4,7,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [1,5,6,4,7,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [1,5,6,4,7,8,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [1,5,6,7,4,3,2,8] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,5,6,7,4,3,8,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,5,6,7,8,4,3,2] => [.,[[[[.,.],.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,5,7,6,8,4,3,2] => [.,[[[[.,.],.],.],[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,4),(4,5),(5,7),(6,7),(7,3)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,5,8,7,6,4,3,2] => [.,[[[[.,.],.],.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,7),(3,7),(5,2),(6,3),(7,4)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [1,6,5,4,3,2,7,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(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] => [1,6,5,4,3,2,8,7] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [1,6,5,4,3,8,7,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [1,6,5,4,7,8,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,6,5,7,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,6,5,7,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,6,5,7,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [1,6,5,8,7,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [1,6,7,5,4,3,2,8] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,6,7,5,4,3,8,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,6,7,5,8,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,6,7,8,5,4,3,2] => [.,[[[[[.,.],.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,6,8,7,5,4,3,2] => [.,[[[[[.,.],.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,7),(4,7),(5,2),(6,5),(7,3)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [1,7,6,5,4,3,2,8] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(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] => [1,7,6,5,4,3,8,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [1,7,6,5,4,8,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,7,6,5,8,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,7,6,8,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,7,8,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,7),(1,6),(2,7),(4,5),(5,2),(6,4),(7,3)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,8,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => ([(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] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [2,1,3,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(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] => [2,1,3,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(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] => [2,1,3,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,1,3,4,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(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] => [2,1,3,4,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [2,1,3,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(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] => [2,1,3,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(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] => [2,1,3,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,1,3,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,1,3,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(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] => [2,1,3,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(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] => [2,1,3,5,4,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,1,3,5,4,7,8,6] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,1,3,5,4,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,1,3,5,6,4,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(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] => [2,1,3,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,1,3,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,1,3,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,1,3,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,1,3,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,3,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,1,3,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(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] => [2,1,4,3,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(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] => [2,1,4,3,5,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,4,3,5,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,4,3,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(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] => [2,1,4,3,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(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] => [2,1,4,3,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(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] => [2,1,4,3,6,7,5,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(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] => [2,1,4,3,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(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] => [2,1,4,3,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,4,3,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,4,3,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(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] => [2,1,4,5,3,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,1,4,5,3,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,1,4,5,3,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,1,4,5,6,3,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,4,5,6,7,3,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(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] => [2,1,4,5,6,7,8,3] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,1,4,5,6,8,7,3] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,1,4,5,7,8,6,3] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,1,4,5,8,7,6,3] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,4,6,5,3,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,1,4,6,5,8,7,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,1,4,6,7,5,8,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,1,4,6,7,8,5,3] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,1,4,6,8,7,5,3] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,1,4,7,6,5,8,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,4,7,8,6,5,3] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,1,4,8,7,6,5,3] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,5,4,3,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(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] => [2,1,5,4,3,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(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] => [2,1,5,4,3,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,1,5,4,3,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,1,5,4,6,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,5,4,6,7,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,1,5,4,6,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,1,5,4,6,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,1,5,4,7,6,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,1,5,4,7,8,6,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,1,5,4,8,7,6,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,5,6,4,3,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(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] => [2,1,5,6,4,3,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,1,5,6,4,7,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,1,5,6,4,8,7,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,5,6,7,4,3,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,1,5,6,7,4,8,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,1,5,6,7,8,4,3] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,1,5,6,8,7,4,3] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,1,5,7,6,4,8,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,1,5,7,6,8,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,5,7,8,6,4,3] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,1,5,8,7,6,4,3] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(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] => [2,1,6,5,4,3,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,1,6,5,4,8,7,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,1,6,5,7,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,1,6,5,7,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,1,6,5,8,7,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,6,7,5,4,3,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,1,6,7,5,4,8,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,1,6,7,5,8,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,1,6,7,8,5,4,3] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,1,6,8,7,5,4,3] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,7,6,5,4,3,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(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] => [2,1,7,6,5,4,8,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,1,7,6,5,8,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,1,7,6,8,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,7,8,6,5,4,3] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,1,8,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => ([(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] => [2,3,1,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [2,3,1,4,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [2,3,1,4,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [2,3,1,4,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [2,3,1,4,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [2,3,1,4,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,3,1,5,4,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0] => [2,3,1,5,6,4,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0] => [2,3,1,5,6,7,4,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,6,8,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,3,1,5,7,8,6,4] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0] => [2,3,1,6,5,4,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0] => [2,3,1,6,5,4,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0] => [2,3,1,6,5,7,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0] => [2,3,1,6,5,8,7,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0] => [2,3,1,6,7,5,4,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,6,7,5,8,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0] => [2,3,1,6,7,8,5,4] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0] => [2,3,1,6,8,7,5,4] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,7,6,5,8,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0] => [2,3,1,7,6,8,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [2,3,1,7,8,6,5,4] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,3,1,8,7,6,5,4] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,3,4,1,5,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [2,3,4,1,5,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,3,4,1,5,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [2,3,4,1,5,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [2,3,4,1,6,5,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [2,3,4,1,6,5,8,7] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [2,3,4,1,6,7,5,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [2,3,4,1,6,7,8,5] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [2,3,4,1,6,8,7,5] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [2,3,4,1,7,6,5,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [2,3,4,1,7,6,8,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [2,3,4,1,7,8,6,5] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,1,8,7,6,5] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [2,3,4,5,1,6,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,1,7,6,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,1,7,8,6] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [2,3,4,5,1,8,7,6] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,1,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,1,8,7] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,1,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [2,3,4,5,6,7,8,1] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,8,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,7,6,1,8] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,7,6,8,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,7,8,6,1] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,7),(5,4),(6,3)],8)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,8,7,6,1] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [2,3,4,6,5,1,7,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [2,3,4,6,5,7,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [2,3,4,6,5,7,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [2,3,4,6,5,8,7,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0] => [2,3,4,6,7,5,1,8] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [2,3,4,6,7,5,8,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [2,3,4,6,7,8,5,1] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [2,3,4,6,8,7,5,1] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [2,3,4,7,6,5,1,8] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [2,3,4,7,6,5,8,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0] => [2,3,4,7,6,8,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [2,3,4,7,8,6,5,1] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,7),(1,6),(2,3),(3,7),(4,5),(5,6),(7,4)],8)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,8,7,6,5,1] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [2,3,5,4,1,6,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [2,3,5,4,1,6,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,4,1,7,6,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,4,1,8,7,6] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [2,3,5,4,6,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [2,3,5,4,6,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [2,3,5,4,6,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [2,3,5,4,7,6,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [2,3,5,4,7,8,6,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [2,3,5,4,8,7,6,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0] => [2,3,5,6,4,1,7,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0] => [2,3,5,6,4,1,8,7] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0] => [2,3,5,6,4,7,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [2,3,5,6,4,7,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [2,3,5,6,4,8,7,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0] => [2,3,5,6,7,4,1,8] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [2,3,5,6,7,4,8,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [2,3,5,6,7,8,4,1] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [2,3,5,6,8,7,4,1] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [2,3,5,7,6,4,1,8] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0] => [2,3,5,7,6,4,8,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,7,6,8,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,7,8,6,4,1] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,8,7,6,4,1] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [2,3,6,5,4,1,7,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [2,3,6,5,4,1,8,7] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [2,3,6,5,4,7,8,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0] => [2,3,6,5,7,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,6,5,8,7,4,1] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [2,3,6,7,5,4,1,8] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [2,3,6,7,8,5,4,1] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,7),(4,7),(5,6),(7,5)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,3,7,6,5,4,1,8] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,7,6,5,4,8,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,6,5,8,4,1] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => ([(0,7),(1,6),(2,3),(3,5),(4,7),(5,6),(6,4)],8)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,8,7,6,5,4,1] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,4,3,1,5,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [2,4,3,1,5,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [2,4,3,1,6,5,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,4,3,1,6,7,8,5] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [2,4,3,1,6,8,7,5] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [2,4,3,1,7,6,8,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [2,4,3,1,7,8,6,5] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [2,4,3,1,8,7,6,5] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [2,4,3,5,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0] => [2,4,3,5,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0] => [2,4,3,5,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [2,4,3,5,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [2,4,3,5,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,4,3,5,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [2,4,3,5,6,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,4,3,5,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [2,4,3,5,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,4,3,5,7,6,8,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [2,4,3,6,5,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [2,4,3,6,5,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0] => [2,4,3,6,5,7,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,4,3,6,5,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,4,3,6,7,5,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [2,4,3,6,7,8,5,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [2,4,3,6,8,7,5,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0] => [2,4,3,7,6,5,8,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,4,3,8,7,6,5,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,4,5,3,1,6,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0] => [2,4,5,3,1,6,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [2,4,5,3,1,7,6,8] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => [2,4,5,3,1,7,8,6] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,4,5,3,1,8,7,6] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0] => [2,4,5,3,6,1,8,7] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,4,5,3,6,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0] => [2,4,5,3,6,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [2,4,5,3,7,8,6,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [2,4,5,3,8,7,6,1] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,4,5,6,3,1,7,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0] => [2,4,5,6,3,7,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [2,4,5,6,3,7,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [2,4,5,6,3,8,7,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,4,5,6,7,3,1,8] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,4,5,6,7,3,8,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,4,5,6,7,8,3,1] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [2,4,5,6,8,7,3,1] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,4,5,7,8,6,3,1] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,7),(3,5),(4,7),(6,4),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [2,4,6,5,3,1,7,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [2,4,6,5,3,1,8,7] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0] => [2,4,6,5,3,7,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,4,6,5,3,8,7,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [2,4,6,5,7,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,4,6,5,7,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,4,6,5,8,7,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [2,4,6,7,5,3,1,8] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,4,6,7,5,3,8,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,4,6,7,5,8,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [2,4,6,7,8,5,3,1] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,4,6,8,7,5,3,1] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,4,7,8,6,5,3,1] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,4,8,7,6,5,3,1] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [2,5,4,3,1,6,7,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0] => [2,5,4,3,1,6,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [2,5,4,3,1,7,6,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [2,5,4,3,1,7,8,6] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [2,5,4,3,1,8,7,6] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [2,5,4,3,6,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [2,5,4,3,6,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,5,4,3,6,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [2,5,4,3,6,8,7,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [2,5,4,3,7,6,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [2,5,4,3,7,8,6,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,5,4,3,8,7,6,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [2,5,4,6,3,7,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,5,4,6,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0] => [2,5,4,6,7,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,5,4,6,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,5,4,7,6,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,5,4,7,6,3,8,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,5,4,7,6,8,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,5,4,7,8,6,3,1] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,5,4,8,7,6,3,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,5,6,4,3,1,8,7] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [2,5,6,4,3,7,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,5,6,4,7,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,5,6,4,7,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,5,6,4,8,7,3,1] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,5,6,7,4,3,1,8] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,5,6,7,4,3,8,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,5,6,7,4,8,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,5,6,7,8,4,3,1] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,5,7,6,4,3,1,8] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,6),(3,4),(4,7),(5,7),(7,6)],8)
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,5,8,7,6,4,3,1] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,6,5,4,3,1,8,7] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,6,5,4,3,7,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,6,5,4,3,8,7,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,6,5,4,7,8,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,6,5,4,8,7,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,6,5,7,4,3,8,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,6,7,5,4,3,1,8] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,6,7,5,8,4,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,6,7,8,5,4,3,1] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,6,8,7,5,4,3,1] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,7),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,7,6,5,4,3,1,8] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,7,6,5,4,3,8,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,7,6,5,4,8,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,7,6,8,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,7,8,6,5,4,3,1] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,8,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(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] => [3,2,1,4,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(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] => [3,2,1,4,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(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] => [3,2,1,4,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [3,2,1,4,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [3,2,1,4,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [3,2,1,4,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [3,2,1,4,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(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] => [3,2,1,4,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [3,2,1,4,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [3,2,1,4,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(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] => [3,2,1,5,4,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(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] => [3,2,1,5,4,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [3,2,1,5,6,4,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(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] => [3,2,1,5,6,7,8,4] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [3,2,1,5,6,8,7,4] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [3,2,1,5,7,6,4,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [3,2,1,5,7,6,8,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [3,2,1,5,7,8,6,4] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [3,2,1,5,8,7,6,4] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [3,2,1,6,5,4,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(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] => [3,2,1,6,5,4,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(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] => [3,2,1,6,5,7,4,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [3,2,1,6,5,7,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [3,2,1,6,5,8,7,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [3,2,1,6,7,5,8,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,6,7,8,5,4] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [3,2,1,6,8,7,5,4] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [3,2,1,7,6,5,4,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(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] => [3,2,1,7,6,5,8,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [3,2,1,7,6,8,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,1,7,8,6,5,4] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,2,1,8,7,6,5,4] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => ([(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] => [3,2,4,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [3,2,4,1,5,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [3,2,4,1,5,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [3,2,4,1,5,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0] => [3,2,4,1,5,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [3,2,4,1,6,5,7,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [3,2,4,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [3,2,4,1,6,7,5,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [3,2,4,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [3,2,4,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0] => [3,2,4,1,7,6,5,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [3,2,4,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [3,2,4,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [3,2,4,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [3,2,4,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [3,2,4,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [3,2,4,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [3,2,4,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [3,2,4,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0] => [3,2,4,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0] => [3,2,4,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0] => [3,2,4,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0] => [3,2,4,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,2,4,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [3,2,5,4,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [3,2,5,4,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [3,2,5,4,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0] => [3,2,5,4,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [3,2,5,4,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0] => [3,2,5,4,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [3,2,5,4,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0] => [3,2,5,4,6,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [3,2,5,4,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0] => [3,2,5,6,4,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0] => [3,2,5,6,4,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [3,2,5,6,7,4,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0] => [3,2,5,6,7,4,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [3,2,5,6,7,8,4,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [3,2,5,7,6,4,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0] => [3,2,5,7,6,4,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [3,2,5,7,6,8,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,5,7,8,6,4,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [3,2,6,5,4,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [3,2,6,5,4,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [3,2,6,5,4,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [3,2,6,5,7,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0] => [3,2,6,5,7,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [3,2,6,7,5,4,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0] => [3,2,6,7,5,4,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => [3,2,6,7,5,8,4,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,2,6,8,7,5,4,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [3,2,7,6,5,4,1,8] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [3,2,7,6,5,4,8,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,7,8,6,5,4,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,2,8,7,6,5,4,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [3,4,2,1,6,5,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [3,4,2,1,6,7,8,5] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [3,4,2,1,6,8,7,5] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [3,4,2,1,7,6,8,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [3,4,2,1,7,8,6,5] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [3,4,2,1,8,7,6,5] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [3,4,2,5,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0] => [3,4,2,5,1,7,8,6] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [3,4,2,5,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0] => [3,4,2,5,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [3,4,2,5,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [3,4,2,5,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0] => [3,4,2,5,6,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [3,4,2,5,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0] => [3,4,2,5,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [3,4,2,5,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0] => [3,4,2,5,8,7,6,1] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0] => [3,4,2,6,5,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0] => [3,4,2,6,5,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [3,4,2,6,5,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0] => [3,4,2,6,5,8,7,1] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0] => [3,4,2,6,7,5,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [3,4,2,6,7,5,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [3,4,2,7,6,5,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0] => [3,4,2,7,6,5,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [3,4,2,7,8,6,5,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,2,8,7,6,5,1] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [3,4,5,2,1,6,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [3,4,5,2,1,7,6,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [3,4,5,2,1,8,7,6] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [3,4,5,2,6,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [3,4,5,2,6,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [3,4,5,2,6,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [3,4,5,2,6,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [3,4,5,2,7,6,1,8] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0] => [3,4,5,2,7,6,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0] => [3,4,5,2,7,8,6,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,2,1,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(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] => [3,4,5,6,2,1,8,7] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(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] => [3,4,5,6,2,7,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [3,4,5,6,2,7,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [3,4,5,6,2,8,7,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,2,1,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,2,8,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,8,7,2,1] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [3,4,5,7,6,2,8,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [3,4,5,7,6,8,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [3,4,5,7,8,6,2,1] => [[[.,.],.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,7),(4,5),(5,7),(6,4)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [3,4,6,5,2,1,8,7] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [3,4,6,5,2,7,1,8] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [3,4,6,5,2,7,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0] => [3,4,6,5,7,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [3,4,6,5,7,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [3,4,6,7,5,2,8,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [3,4,6,7,5,8,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [3,4,6,7,8,5,2,1] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [3,4,7,6,5,2,1,8] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [3,4,7,6,5,2,8,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [3,4,7,6,5,8,2,1] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,6),(5,7),(6,5)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [3,5,4,2,1,6,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [3,5,4,2,1,6,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [3,5,4,2,1,7,6,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [3,5,4,2,1,7,8,6] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [3,5,4,2,1,8,7,6] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0] => [3,5,4,2,6,1,7,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(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] => [3,5,4,2,6,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(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] => [3,5,4,2,6,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [3,5,4,2,6,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [3,5,4,2,7,6,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [3,5,4,2,7,6,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [3,5,4,2,7,8,6,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [3,5,4,6,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [3,5,4,6,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [3,5,4,6,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [3,5,4,6,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [3,5,4,7,6,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0] => [3,5,4,7,6,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [3,5,4,7,6,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [3,5,4,7,8,6,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [3,5,6,4,2,1,8,7] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [3,5,6,4,2,7,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [3,5,6,4,2,7,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [3,5,6,4,2,8,7,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [3,5,6,4,7,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [3,5,6,4,7,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [3,5,6,4,7,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [3,5,6,7,4,2,1,8] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [3,5,6,7,4,2,8,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [3,5,6,7,4,8,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [3,5,6,7,8,4,2,1] => [[[.,.],.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,5,6,8,7,4,2,1] => [[[.,.],.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [3,5,7,6,4,2,1,8] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0] => [3,5,7,6,4,2,8,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0] => [3,5,7,6,4,8,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [3,5,7,6,8,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,5,7,8,6,4,2,1] => [[[.,.],.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,7),(5,6),(6,7)],8)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,5,8,7,6,4,2,1] => [[[.,.],.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [3,6,5,4,2,1,7,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [3,6,5,4,2,1,8,7] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [3,6,5,4,2,7,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [3,6,5,4,2,7,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [3,6,5,4,2,8,7,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [3,6,5,4,7,2,1,8] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [3,6,5,4,7,2,8,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [3,6,5,4,7,8,2,1] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [3,6,5,4,8,7,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,6,8,7,5,4,2,1] => [[[.,.],.],[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(2,5),(3,7),(4,7),(5,6),(7,6)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [3,7,6,5,4,8,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [3,7,6,5,8,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,7,6,8,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,7,8,6,5,4,2,1] => [[[.,.],.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,3),(2,4),(3,7),(4,5),(5,6),(6,7)],8)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [4,3,2,1,5,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(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] => [4,3,2,1,5,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(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] => [4,3,2,1,5,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [4,3,2,1,5,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(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] => [4,3,2,1,6,5,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(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] => [4,3,2,1,6,5,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(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] => [4,3,2,1,6,7,5,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(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] => [4,3,2,1,6,7,8,5] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [4,3,2,1,6,8,7,5] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [4,3,2,1,7,6,5,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(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] => [4,3,2,1,7,6,8,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [4,3,2,1,7,8,6,5] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,3,2,1,8,7,6,5] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(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] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [4,3,2,5,1,7,8,6] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [4,3,2,5,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [4,3,2,5,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0] => [4,3,2,5,6,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [4,3,2,5,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0] => [4,3,2,5,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0] => [4,3,2,5,7,8,6,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,3,2,5,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [4,3,2,6,5,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [4,3,2,6,5,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [4,3,2,6,5,7,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0] => [4,3,2,6,5,7,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0] => [4,3,2,6,5,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [4,3,2,6,7,5,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0] => [4,3,2,6,7,5,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [4,3,2,6,8,7,5,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [4,3,2,7,6,5,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [4,3,2,7,8,6,5,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,3,2,8,7,6,5,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [4,3,5,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [4,3,5,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [4,3,5,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [4,3,5,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0] => [4,3,5,2,7,6,8,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [4,3,5,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [4,3,5,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [4,3,5,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [4,3,5,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [4,3,5,7,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [4,3,6,5,2,1,7,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [4,3,6,5,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [4,3,6,5,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [4,3,6,5,7,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0] => [4,3,6,5,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [4,3,6,5,7,8,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,3,6,5,8,7,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0] => [4,3,6,7,5,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [4,3,6,7,8,5,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [4,3,7,6,5,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [4,3,7,6,5,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [4,3,7,6,5,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,7,8,6,5,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [4,3,8,7,6,5,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [4,5,3,2,1,6,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(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] => [4,5,3,2,1,7,6,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [4,5,3,2,1,8,7,6] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(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] => [4,5,3,2,6,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [4,5,3,2,6,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [4,5,3,2,7,6,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [4,5,3,2,8,7,6,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [4,5,3,6,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [4,5,3,6,2,7,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [4,5,3,6,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,6,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [4,5,3,7,6,8,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,5,3,7,8,6,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [4,5,6,3,2,1,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [4,5,6,3,2,1,8,7] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [4,5,6,3,2,8,7,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [4,5,6,3,8,7,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [4,5,6,7,3,2,1,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,6,8,7,3,2,1] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [4,5,7,6,3,2,1,8] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,5,7,6,8,3,2,1] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,7),(5,7),(6,4)],8)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [4,5,8,7,6,3,2,1] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [4,6,5,3,2,1,8,7] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [4,6,5,3,2,8,7,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [4,6,5,3,7,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [4,6,5,7,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0] => [4,6,5,7,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,6,5,7,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,6,5,8,7,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [4,6,7,5,3,2,1,8] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [4,6,7,5,3,2,8,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,6,7,5,8,3,2,1] => [[[[.,.],.],.],[[.,.],[.,[.,.]]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [4,6,8,7,5,3,2,1] => [[[[.,.],.],.],[[.,.],[[.,.],.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [4,7,6,5,3,2,1,8] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [4,7,6,5,3,2,8,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [4,7,6,5,3,8,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,7,6,5,8,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,7,6,8,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [4,7,8,6,5,3,2,1] => [[[[.,.],.],.],[[[.,.],.],[.,.]]] => ([(0,7),(1,3),(2,4),(3,7),(4,5),(5,6),(7,6)],8)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [4,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(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] => [5,4,3,2,1,6,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(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] => [5,4,3,2,1,7,6,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(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] => [5,4,3,2,1,7,8,6] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,4,3,2,1,8,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(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] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [5,4,3,2,6,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,4,3,2,6,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [5,4,3,2,7,6,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [5,4,3,2,7,6,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [5,4,3,2,7,8,6,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,4,3,2,8,7,6,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [5,4,3,6,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [5,4,3,6,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0] => [5,4,3,6,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0] => [5,4,3,6,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [5,4,3,6,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [5,4,3,7,6,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [5,4,3,7,6,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [5,4,3,7,8,6,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [5,4,3,8,7,6,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [5,4,6,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [5,4,6,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [5,4,6,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [5,4,6,3,2,7,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,4,6,3,2,8,7,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [5,4,6,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [5,4,7,6,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,4,7,6,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,4,7,6,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [5,4,7,8,6,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [5,6,4,3,2,1,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [5,6,4,3,2,1,8,7] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [5,6,4,3,2,7,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [5,6,4,3,7,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,4,3,8,7,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [5,6,4,7,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [5,6,4,8,7,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [5,6,7,4,3,2,1,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [5,6,7,4,3,2,8,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [5,6,8,7,4,3,2,1] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [5,7,6,4,3,2,1,8] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [5,7,6,4,3,2,8,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,7,6,4,3,8,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,7,6,4,8,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [5,7,6,8,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [5,7,8,6,4,3,2,1] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [5,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(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] => [6,5,4,3,2,1,8,7] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(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] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,5,4,3,2,8,7,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [6,5,4,3,8,7,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,5,4,7,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [6,5,8,7,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [6,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(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] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => ([(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] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(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] => [1,9,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(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] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(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] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1,8,9,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => ([(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] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(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] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [1,8,7,9,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,7,9,8,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1,9,10,8,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,11,10,9,8,7,6,5,4,3,2] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => ([(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] => [8,7,9,6,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [7,6,5,8,4,3,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [6,7,8,5,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [1,7,8,9,6,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [1,9,8,10,7,6,5,4,3,2] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [8,7,6,9,5,4,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [7,8,9,6,5,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [6,7,5,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [1,8,9,10,7,6,5,4,3,2] => [.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] => ([(0,8),(1,4),(2,9),(4,9),(5,7),(6,5),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [7,6,5,4,3,8,2,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0] => [6,5,7,8,4,3,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [1,7,6,8,9,5,4,3,2] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [8,7,6,5,4,9,3,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,1,0] => [7,6,8,9,5,4,3,2,1,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,8,7,6,5,4,3,1,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,6,5,4,3,2,1,9,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,1,9,8,7,6,5,4,3] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(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] => [1,3,9,8,7,6,5,4,2] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [8,7,6,5,4,3,9,2,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [1,8,7,6,5,4,3,2,9] => [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,8,9,7,6,5,4,3] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,9,8,7,6,5,4,3] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => ([(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] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,7,6,5,4,3,2,1,10,9] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [1,7,8,6,5,4,3,2,9] => [.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,1,10,9,8,7,6,5,4,3] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(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] => [1,3,10,9,8,7,6,5,4,2] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(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] => [1,9,8,7,6,5,4,3,2,10] => [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1,0] => [6,5,4,3,7,8,2,1,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,10,9,8,7,6,5,4,3] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => ([(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] => [2,3,4,5,6,7,8,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [2,3,4,5,6,8,7,9,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [2,3,4,5,6,8,9,7,1] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,9,8,7,1] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,9,8,7,6,5,4,1] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,8,7,6,5,4,3,9,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,8,7,9,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,8,9,7,6,5,4,3,1] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(0,8),(1,7),(2,6),(3,7),(4,5),(5,3),(6,4),(7,8)],9)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [3,2,4,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,2,9,8,7,6,5,4,1] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [3,4,2,5,6,7,8,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,2,9,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,9,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [4,5,6,3,7,8,9,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [4,9,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,4,3,2,9,8,7,6,1] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [5,4,6,7,8,3,9,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [5,6,4,7,3,8,2,9,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [5,9,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [6,5,4,9,8,7,3,2,1] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [6,9,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,6,5,4,3,2,9,8,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,6,8,5,4,3,2,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [7,6,8,5,9,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [7,6,8,9,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [7,6,9,8,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,8,6,5,4,3,2,9,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [7,9,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => ([(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] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [1,2,3,4,5,6,7,9,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(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] => [1,2,3,4,5,6,8,9,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => ([(0,8),(1,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(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] => [1,2,3,4,5,6,7,8,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => ([(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] => [1,2,3,4,5,6,9,8,7] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(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] => [1,2,3,4,5,6,7,9,10,8] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => ([(0,9),(1,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,3,4,5,8,7,9,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,3,4,5,6,8,9,10,7] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,2,3,4,5,7,8,9,10,6] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,4,6,7,8,9,10,5] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,3),(5,6),(6,2),(7,4),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,3,5,6,7,8,9,10,4] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [1,4,3,5,6,7,8,9,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,2,4,5,6,7,8,9,10,3] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,7,8,9,10,2] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,5,6,7,8,9,11,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => ([(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] => [1,2,3,4,5,6,7,10,9,8] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => ([(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] => [1,2,3,4,5,6,7,8,10,11,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,3,4,5,8,9,7,6] => [.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,9,8,7,6] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => ([(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] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,4,5,6,7,8,11,10,9] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,3,4,5,6,10,9,8,7] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,9,8,7,6,5] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => ([(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] => [1,2,3,4,5,10,9,8,7,6] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => ([(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] => [1,4,5,6,7,8,3,9,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [3,4,5,6,2,7,8,9,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,7,8,9,10,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [1,4,5,6,7,8,9,3,2] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,9,8,7,6,5,4] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,10,9,8,7,6,5] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [3,4,5,6,7,8,9,2,10,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,8,7,9] => [.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] => ([(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] => [1,2,3,4,5,7,6,8,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => ([(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] => [1,2,3,4,5,7,6,9,8] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => ([(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] => [1,2,3,4,6,5,7,8,9] => [.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] => ([(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] => [1,2,3,4,6,5,8,7,9] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => ([(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] => [1,2,3,4,6,5,9,8,7] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => ([(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] => [1,2,3,5,4,6,7,8,9] => [.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] => ([(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] => [1,2,3,5,4,9,8,7,6] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => ([(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] => [1,2,4,3,5,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [1,2,4,3,9,8,7,6,5] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => ([(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] => [1,3,2,4,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [1,3,2,4,5,6,7,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(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] => [1,3,2,5,4,6,7,8,9] => [.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,3,2,9,8,7,6,5,4] => [.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] => ([(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] => [1,4,3,2,5,6,7,8,9] => [.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [1,7,6,5,4,3,2,9,8] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => ([(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] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [2,1,3,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(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] => [2,1,3,4,5,6,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,8,7,6,5,4,3,9] => [[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] => ([(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] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,2,1,9,8,7,6,5,4] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => ([(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] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,3,2,1,9,8,7,6,5] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => ([(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] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [5,4,3,2,1,9,8,7,6] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => ([(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] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(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] => [6,5,4,3,2,1,9,8,7] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => ([(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] => [1,2,3,4,5,6,7,9,8,10] => [.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] => ([(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] => [1,2,3,4,5,6,8,7,9,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => ([(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] => [1,2,3,4,5,7,6,8,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(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] => [1,2,3,4,6,5,7,8,9,10] => [.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [1,2,3,5,4,6,7,8,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [1,2,3,10,9,8,7,6,5,4] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => ([(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] => [1,2,4,3,5,6,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [1,3,2,4,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [1,3,2,5,4,7,6,9,8,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => ([(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] => [1,3,2,10,9,8,7,6,5,4] => [.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(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] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(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] => [2,1,3,4,5,6,7,8,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(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] => [2,1,4,3,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(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] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [3,2,1,10,9,8,7,6,5,4] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(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] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [4,3,2,1,10,9,8,7,6,5] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => ([(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] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(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] => [5,4,3,2,1,10,9,8,7,6] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => ([(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] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(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] => [6,5,4,3,2,1,10,9,8,7] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => ([(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] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(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] => [7,6,5,4,3,2,1,10,9,8] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => ([(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] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => ([(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] => [2,3,1,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [2,3,4,5,6,7,8,1,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(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] => [2,3,1,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [2,3,4,5,6,8,7,1,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(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] => [2,3,4,5,6,7,8,9,1,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,6,7,8,9,10,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(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] => [2,1,3,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,5,6,7,8,10,9,1] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [8,10,9,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [9,11,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => ([(0,9),(1,3),(2,10),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [8,7,9,10,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,3,1,4,5,6,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,3,1,4,5,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [3,4,5,6,7,8,2,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [3,4,5,6,7,2,1,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(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] => [3,4,5,6,2,1,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,10,9,8,7,6,5,4,3,1] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,9,7,6,5,4,3,2,10,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [6,5,4,3,2,7,1,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [5,4,3,2,6,1,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,3,2,5,1,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [7,10,9,8,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [6,10,9,8,7,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [5,10,9,8,7,6,4,3,2,1] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [4,10,9,8,7,6,5,3,2,1] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [3,10,9,8,7,6,5,4,2,1] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,1,9,8,7,6,5,4] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,3,4,5,2,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,3,6,7,8,9] => [.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [1,2,3,4,5,7,8,6,9,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,2),(7,3),(8,5),(9,8)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,9,6,10] => [.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] => ([(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] => [2,3,4,5,1,6,7,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,2,4,5,6,7,8,1,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [1,3,4,5,6,7,9,8,2] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,1,9,8] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(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] => [2,3,4,5,6,1,9,8,7] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [2,3,4,5,6,7,10,9,8,1] => [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1,9,8,7,6] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [2,3,4,5,6,1,8,7,9] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,3,1,6,5,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,8,7,10,9,1] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [8,7,10,9,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [7,6,5,10,9,8,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,10,9,8,7,2,1] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [1,3,5,7,9,10,8,6,4,2] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,9),(3,7),(4,8),(6,8),(7,9),(8,7),(9,5)],10)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => ([(0,10),(2,3),(3,5),(4,2),(5,7),(6,4),(7,9),(8,6),(9,1),(10,8)],11)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,3,1,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,2,4,9,8,7,6,5,3] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,3),(6,4),(7,2),(8,7)],9)
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,2,3,5,9,8,7,6,4] => [.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] => ([(0,8),(1,6),(3,8),(4,3),(5,2),(6,4),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [1,2,3,4,6,9,8,7,5] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => ([(0,8),(1,6),(3,8),(4,5),(5,2),(6,3),(7,4),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,3,4,5,7,9,8,6] => [.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0] => [9,8,7,6,5,4,3,2,1,11,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => ([(0,9),(1,3),(2,10),(3,10),(4,6),(5,4),(6,8),(7,5),(8,2),(9,7)],11)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0] => [4,5,3,2,1,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,4,5,6,7,8,10,9,11] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]] => ([(0,10),(1,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7),(10,9)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,7,8,6,9] => [.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] => ([(0,8),(1,3),(3,8),(4,6),(5,4),(6,2),(7,5),(8,7)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,3,4,5,6,8,9,7,10] => [.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] => ([(0,9),(1,3),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,8)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [1,3,4,5,6,7,2,9,8] => [.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [3,4,2,5,1,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9)
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,6,7,8,9,10,1,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,10),(3,4),(4,6),(5,3),(6,8),(7,5),(8,2),(9,7)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,2,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,7,6,5,4,3,2,10,9,1] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,2,10,9,8,7,6,5,4,1] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,2,3,4,6,8,9,7,5] => [.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] => ([(0,8),(1,7),(2,7),(4,6),(5,4),(6,3),(7,8),(8,5)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [3,4,5,2,1,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,4,2,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,5,6,7,8,1,10,9] => [[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [2,3,4,5,6,1,8,9,7] => [[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,4),(6,3),(8,5)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [5,6,4,3,2,1,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0] => [5,6,4,3,2,7,1,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0] => [6,7,5,4,3,2,1,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,3,4,2,5,6,7,8,9,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [1,3,4,5,6,7,8,9,2,10] => [.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,9),(4,5),(5,7),(6,4),(7,2),(8,6),(9,3)],10)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,2,4,5,6,3,7,8,9,10] => [.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2),(9,8)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,2,3,5,6,7,8,4,9,10] => [.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,7),(3,9),(4,5),(5,3),(6,2),(7,4),(8,6),(9,8)],10)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [1,7,6,5,4,3,9,8,2] => [.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] => ([(0,7),(1,4),(2,8),(4,8),(5,6),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,10,1] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,9,10,1] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,10,8] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,9),(3,7),(4,8),(6,8),(7,9),(8,7),(9,5)],10)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,2,4,1,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [1,3,4,5,6,7,2,8,9] => [.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(4,6),(5,4),(6,2),(7,5),(8,3)],9)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [6,5,7,4,8,3,9,2,10,1] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],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] => [2,1,4,3,6,5,8,7,10,9,12,11] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] => ([(0,7),(1,11),(2,9),(3,10),(4,8),(5,6),(6,11),(7,10),(9,8),(10,9),(11,7)],12)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [2,1,4,6,5,3,8,7,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,1,4,3,6,8,7,5,10,9] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,3,6,5,8,10,9,7] => [[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] => ([(0,6),(1,9),(2,7),(3,8),(4,5),(5,9),(6,8),(8,7),(9,6)],10)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [5,4,6,3,7,2,8,1,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0] => [4,5,3,6,2,7,1,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,4,7,6,9,8,11,12,10] => [.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] => ([(0,7),(1,7),(2,11),(3,9),(4,10),(5,8),(7,10),(8,11),(9,8),(10,9),(11,6)],12)
Map
to 312-avoiding permutation
Description
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to poset
Description
Return the poset obtained by interpreting the tree as a Hasse diagram.
searching the database
Sorry, this map was not found in the database.