Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00011: Binary trees —to graph⟶ Graphs
Images
[1,0] => [1] => [.,.] => ([],1)
[1,0,1,0] => [2,1] => [[.,.],.] => ([(0,1)],2)
[1,1,0,0] => [1,2] => [.,[.,.]] => ([(0,1)],2)
[1,0,1,0,1,0] => [3,2,1] => [[[.,.],.],.] => ([(0,2),(1,2)],3)
[1,0,1,1,0,0] => [2,3,1] => [[.,[.,.]],.] => ([(0,2),(1,2)],3)
[1,1,0,0,1,0] => [3,1,2] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[1,1,0,1,0,0] => [2,1,3] => [[.,.],[.,.]] => ([(0,2),(1,2)],3)
[1,1,1,0,0,0] => [1,2,3] => [.,[.,[.,.]]] => ([(0,2),(1,2)],3)
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[[.,[.,.]],.],.] => ([(0,3),(1,2),(2,3)],4)
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[[.,.],[.,.]],.] => ([(0,3),(1,3),(2,3)],4)
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[[.,.],[.,.]],.] => ([(0,3),(1,3),(2,3)],4)
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[.,[.,[.,.]]],.] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4)
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4)
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[[[.,[.,.]],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[[.,[.,.]],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5)
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5)
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[[[[.,.],[.,.]],.],.],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
>>> Load all 1910 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[[[[[.,.],[.,.]],.],.],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[[[[[[[.,.],.],.],.],.],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[[[[[[.,.],[.,.]],.],.],.],.],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[[[[[[.,.],.],[.,.]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[[[[[.,[.,.]],[.,.]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[[[[[.,.],[.,[.,.]]],.],.],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[[[[[.,.],[.,.]],[.,.]],.],.],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[[[[[[.,.],.],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[[[[[.,[.,.]],.],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[[[[[.,.],[.,.]],.],[.,.]],.],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[[[[.,[.,[.,.]]],.],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[[[[.,[.,.]],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[[[[[.,.],.],[.,.]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[[[[.,.],[.,[.,.]]],[.,.]],.],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[[[[.,.],[.,.]],[.,[.,.]]],.],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[[[.,[.,[.,.]]],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[[[[.,[.,.]],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[[[[[.,.],.],.],[.,[.,.]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[[[.,[.,.]],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[[[[.,.],.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,2,3,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,3,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[[[[[.,.],[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,2,6,1] => [[[[[.,[.,.]],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[[[[[.,.],.],.],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[[[[.,.],[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[[[.,[.,[.,.]]],[.,.]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[[[[.,.],.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[[[.,[.,.]],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[[[.,.],[.,[.,[.,.]]]],[.,.]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,2,3,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[[[.,[.,.]],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [[[[[.,.],.],[.,.]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[[[.,.],[.,.]],[.,[.,[.,.]]]],.] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,1,2] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,2,1,3] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[[[[.,[.,.]],[.,.]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [[[[[.,.],[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [[[[.,[.,[.,.]]],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[[[[[.,.],.],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[[[[.,[.,.]],.],[.,.]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[[[[.,.],[.,.]],[.,.]],.],[.,.]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[[[.,[.,.]],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[[[[.,.],.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[[[.,.],[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [[[[.,[.,[.,.]]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[[[[[.,.],.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[[[[.,[.,.]],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[[[[.,.],[.,.]],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [[[[[.,.],.],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[[[.,.],[.,[.,.]]],[.,.]],[.,.]] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8)
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[[.,[.,[.,.]]],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[[[.,.],[.,.]],[.,[.,.]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[[[.,[.,.]],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [[[[[.,.],.],.],[.,[.,.]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[[[.,.],.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,1,2,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[[[[.,[.,.]],.],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [[[[[.,.],[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [[[[.,[.,.]],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[[[[.,.],.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,1,7,8] => [[[[.,.],[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,1,5,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[[[[.,.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[[[.,.],[.,.]],[.,.]],[.,[.,.]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(4,7),(6,7)],8)
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[[.,[.,[.,.]]],[.,.]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[[[.,.],.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[[.,[.,.]],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[[.,.],[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,7),(3,5),(3,7),(4,6),(4,7)],8)
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,1,2,3,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,1,2,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,1,2,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,1,3,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[[[.,.],[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[[[.,.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8)
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [6,5,1,2,3,4,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1,2,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1,3,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [9,3,1,2,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,1,4,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,5,6,7,8,9,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,11,1] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [10,3,1,2,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [9,4,1,2,3,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [10,4,1,2,3,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,4,1,2,5,6,7,8] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,3,6,7,8,9,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [9,6,1,2,3,4,5,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [10,6,1,2,3,4,5,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [9,7,1,2,3,4,5,6,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,1,8] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,7,8,9,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0] => [10,7,1,2,3,4,5,6,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [9,8,1,2,3,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,1,3,4,5,6,7] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [10,9,1,2,3,4,5,6,7,8] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [6,5,4,2,3,7,8,9,1] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [4,3,5,6,7,8,9,10,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,1,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [7,8,6,5,4,3,2,1,9] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [8,6,7,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [7,6,8,5,4,3,2,1,9] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1,9] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,1,9] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1,9] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,1,2,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,1,3,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,3,2,1,4,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [8,7,6,4,3,2,1,5,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [8,7,5,4,3,2,1,6,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,1,7,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,1,8,9] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,2,3,1,4,9] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,1,8,9] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,1,2,3,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,7,1,2,8,9] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [7,6,5,3,2,1,4,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,1,7,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,6,1,7,8,9] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0,0] => [8,7,5,3,1,2,4,6,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0] => [7,5,4,3,1,2,6,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,1,2,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => [8,6,4,2,1,3,5,7,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8,9] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,1,6,7,8,9] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [6,7,8,1,2,3,4,5,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0] => [7,5,3,1,2,4,6,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,1,2,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [4,3,5,1,2,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [4,5,2,1,3,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8,9] => [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,1,4,5,6,7,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8,9] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [7,8,1,2,3,4,5,6,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [8,3,1,2,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1,2,4,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1,3,4,5,6,7,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9] => [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,2,1] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,2,1] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,7,6,9,5,4,3,2,1] => [[[[[[[[.,.],.],[.,.]],.],.],.],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [8,7,6,5,9,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,9,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,9,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,3,2,9,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [7,8,9,6,5,4,3,2,1] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [8,6,7,9,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [9,8,7,10,6,5,4,3,2,1] => [[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [9,8,7,6,10,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,10,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,10,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [8,7,6,5,4,2,3,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,10,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,10,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [10,11,9,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [8,9,10,7,6,5,4,3,2,1] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [10,9,11,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [6,7,8,9,5,4,3,2,1] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,3,1,2,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,11,1] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [10,9,8,7,6,5,4,3,2,1,11] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [7,8,9,10,6,5,4,3,2,1] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,4,2,1,3,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,4,3,2,1] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,5,3,2,1,4,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,5,4,3,2,1] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [8,6,5,4,3,2,7,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,1,5,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,3,2,8,9,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [9,8,7,5,4,3,2,1,6,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,2,1] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [9,8,6,5,4,3,2,1,7,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,4,3,2,1] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,1,2,3,4,5,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [9,7,6,5,4,3,2,1,8,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,2,1] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [8,9,6,7,5,4,3,2,1] => [[[[[[[.,[.,.]],[.,.]],.],.],.],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [9,6,7,8,5,4,3,2,1] => [[[[[[[.,.],[.,[.,.]]],.],.],.],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,4,3,2,1] => [[[[[[[[.,.],.],.],[.,.]],.],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,3,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,3,1] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,4,1] => [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [8,9,2,3,4,5,6,7,1] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,3,1,2] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,3,1,2] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [9,7,8,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,3,1,2] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,4,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,1,2,3] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,5,1,2,3] => [[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,1,2,3,4] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0] => [9,8,7,5,6,1,2,3,4] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,1,2,3,4,5] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0] => [7,8,9,6,1,2,3,4,5] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0] => [9,8,6,7,1,2,3,4,5] => [[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [9,8,7,1,2,3,4,5,6] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0] => [9,7,8,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [10,8,9,7,6,5,4,3,2,1] => [[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [10,9,8,6,7,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,6,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,3,2,1] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,3,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,2,3,1] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,5,6,3,4,1,2] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,9),(2,8),(3,5),(4,6),(5,8),(6,9),(7,8),(7,9)],10)
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,1,2] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,1,2,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,1,2,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,1,2,3,4,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,1,2,3,4,5,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [10,9,8,1,2,3,4,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8,9,10] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,4,2,1,3] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,1,4] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,1,5] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,3,2,1,6] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,2,1,7] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,1,8] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,2,1,3] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,3,1,4] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,2,1,4] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,4,3,2,1,5] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [10,9,8,7,5,4,3,2,1,6] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,4,3,2,1,7] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [9,6,7,5,4,3,2,1,8] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,2,1,8] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,1,9] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,1,2,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,1,2,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [11,10,9,8,7,6,5,4,3,1,2] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,3,1,2] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [4,3,1,2,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [9,8,10,7,6,5,4,3,1,2] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,1,3] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,7,9,6,5,4,2,3,1] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] => ([(0,7),(1,7),(2,8),(3,8),(4,6),(4,8),(5,6),(5,7)],9)
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [8,9,7,6,5,4,2,1,3] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,1,7,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [9,8,5,4,3,2,1,6,7] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [9,8,7,4,3,2,1,5,6] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,3,2,1,4,5] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,2,1,3,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [10,1,2,3,4,5,6,7,8,9,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [9,2,1,3,4,5,6,7,8,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [9,8,6,1,2,3,4,5,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,1,2,3,4,6] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,1,2,3,5] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,1,2,4] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [9,6,5,4,3,2,7,1,8] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10,11] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,1,3] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,2,1,3,4] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,2,1,3,4,5] => [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,2,1,3,4,5,6] => [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,2,5,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [10,9,7,6,8,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [10,8,7,6,9,5,4,3,2,1] => [[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [8,9,7,6,4,3,2,1,5] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [9,8,7,6,4,3,5,1,2] => [[[[[[[.,.],.],.],.],.],[.,.]],[.,.]] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,2,3,8,9,1] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,1,2,8] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [8,9,6,5,4,3,2,1,7] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,4,3,2,1,5] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [7,6,5,4,3,2,1,8,9,10] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [8,7,9,1,2,3,4,5,6] => [[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [9,7,8,5,4,3,2,1,6] => [[[[[[[.,.],[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [9,10,6,7,4,5,2,3,1,8] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,9),(2,8),(3,5),(4,6),(5,8),(6,9),(7,8),(7,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,1,9,10] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8,9,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [4,5,6,1,2,3,7,8,9,10] => [[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,1,2,3,4,9,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0] => [6,7,8,9,1,2,3,4,5,10] => [[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [10,8,6,4,2,1,3,5,7,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [10,7,6,5,4,3,2,1,8,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0] => [9,5,4,3,2,1,6,7,8] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,1,7,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [9,8,7,6,5,3,2,4,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8,9,10] => [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [11,9,10,8,7,6,5,4,3,2,1] => [[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.] => ([(0,9),(1,10),(2,10),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,9,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1,6,7,8,9,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,1,5,6,7,8,9,10] => [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [11,9,8,7,6,5,4,3,2,1,10] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => ([(0,10),(1,9),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9),(8,10)],11)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,2,8,1] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => ([(0,7),(1,8),(2,8),(3,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [8,9,1,2,3,4,5,6,7,10] => [[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2,10] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,4,3,2,1,5,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,1,2,3,4,7] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0] => [9,8,4,1,2,3,5,6,7] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [9,8,7,5,4,6,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [10,9,8,6,5,7,4,3,2,1] => [[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.] => ([(0,8),(1,7),(2,9),(3,5),(3,7),(4,6),(4,8),(5,9),(6,9)],10)
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,2,9,1] => [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,3,7,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,8,3,2,1] => [[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.] => ([(0,7),(1,8),(2,9),(3,4),(3,5),(4,8),(5,9),(6,7),(6,9)],10)
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [9,8,6,5,4,7,3,2,1] => [[[[[[[[.,.],.],.],.],[.,.]],.],.],.] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [10,9,7,6,5,4,3,8,2,1] => [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,3,1,2,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [9,7,6,5,4,3,8,2,1] => [[[[[[[[.,.],.],.],.],.],[.,.]],.],.] => ([(0,7),(1,6),(2,8),(3,4),(3,5),(4,6),(5,8),(7,8)],9)
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9,10] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [10,7,8,6,5,4,3,2,1,9] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,1,10] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,9),(3,4),(3,5),(4,6),(5,7),(6,9),(8,9)],10)
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => [9,7,5,3,1,2,4,6,8,10] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],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] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,11),(1,10),(2,8),(3,9),(4,6),(5,7),(6,10),(7,11),(8,9),(8,10),(9,11)],12)
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [10,8,9,6,5,4,3,2,1,7] => [[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,9),(2,9),(3,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [5,6,4,7,3,8,2,9,1,10] => [[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]] => ([(0,7),(1,9),(2,8),(3,5),(4,6),(5,8),(6,9),(7,8),(7,9)],10)
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [10,8,7,6,5,4,2,1,3,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => [9,7,5,3,1,2,4,6,8] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => ([(0,8),(1,7),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8)],9)
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [10,8,6,5,4,3,2,1,7,9] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => ([(0,9),(1,8),(2,3),(2,4),(3,5),(4,6),(5,7),(6,8),(7,9)],10)
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0] => [9,7,5,2,3,1,4,6,8] => [[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,7),(2,8),(3,4),(3,7),(4,8),(5,6),(5,8)],9)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
searching the database
Sorry, this map was not found in the database.