- FindStat

Identifier

Mp00140: Dyck paths —logarithmic height to pruning number⟶ Binary trees
Mp00013: Binary trees —to poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001878: Lattices ⟶ ℤ

Values

[1,0,1,0,1,0] => [.,[.,[.,.]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,0] => [.,[[.,.],.]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,0] => [[.,[.,.]],.] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,0] => [[[.,.],.],.] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,0,0,1,0] => [.,[[.,[.,.]],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,0,1,0,0] => [.,[[[.,.],.],.]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,0,1,0,1,0] => [[.,[.,[.,.]]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,0,1,1,0,0] => [[.,[[.,.],.]],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,0,0,1,0] => [[[.,[.,.]],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,0,1,0,0] => [[[[.,.],.],.],.] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,0,1,1,0,0,1,0] => [.,[.,[[.,[.,.]],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,0,1,1,0,1,0,0] => [.,[.,[[[.,.],.],.]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,1,0,0,1,0,1,0] => [.,[[.,[.,[.,.]]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,.],.]],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,1,0,1,0,0,1,0] => [.,[[[.,[.,.]],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,0,1,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,0,1,0,1,0,1,0] => [[.,[.,[.,[.,.]]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,0,1,0,1,1,0,0] => [[.,[.,[[.,.],.]]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[.,.]],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,0,1,1,0,1,0,0] => [[.,[[[.,.],.],.]],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,1,0,0,1,0,1,0] => [[[.,[.,[.,.]]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,1,0,0,1,1,0,0] => [[[.,[[.,.],.]],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,1,0,1,0,0,1,0] => [[[[.,[.,.]],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],.] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,0,1,0] => [[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,0,1,1,0,0] => [[.,.],[.,[[.,.],.]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,[.,.]],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,1,0,0,0,1,0] => [[.,[.,.]],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,1,0,0,0] => [[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,1,1,0,0,0,0] => [[.,[[.,.],.]],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,0,0,0,0,1,0] => [[[.,.],.],[.,[.,.]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,.],.]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,1,0,0,0] => [[[.,[.,.]],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,.]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,0,1,0,1,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,0,1,1,0,0,1,0] => [.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,0,1,1,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,1,0,0,1,0,1,0] => [.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,1,0,0,1,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,1,0,1,0,0,1,0] => [.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,0,1,1,1,0,0,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,0,0,1,1,0,0] => [.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,0,1,0,0,1,0] => [.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,1,0,0,0,1,0] => [.,[[.,[.,.]],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[.,[.,.]],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,1,0,0,0,0,1,0] => [.,[[[.,.],.],[.,[.,.]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[.,.],.],[[.,.],.]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,1,1,0,0,1,0,0,0] => [.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,0,1,1,0,0,1,0] => [[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,0,1,1,0,1,0,0] => [[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,1,0,0,1,0,1,0] => [[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,1,0,0,1,1,0,0] => [[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,1,0,1,0,0,1,0] => [[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,0,1,1,0,1,0,1,0,0] => [[.,[[[[.,.],.],.],.]],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,0,1,0,1,1,0,0] => [[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,0,1,1,0,0,1,0] => [[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,0,1,1,0,1,0,0] => [[[.,[[[.,.],.],.]],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,1,0,0,1,0,1,0] => [[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,1,0,0,1,1,0,0] => [[[[.,[[.,.],.]],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,1,0,1,0,0,1,0] => [[[[[.,[.,.]],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],.] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,0,1,1,0,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[[.,.],.]],.] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,1,1,0,0,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,1,0,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,0,1,0,1,1,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,0,1,1,0,1,0,0] => [[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,1,0,0,1,0,1,0] => [[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

>>> Load all 488 entries. <<<

[1,1,1,0,0,1,0,0,1,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,1,0,1,0,0,1,0] => [[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,0,0,0,1,0,1,0] => [[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,0,0,1,1,0,0] => [[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,0,1,0,0,1,0] => [[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,0,1,0,1,0,0] => [[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,1,0,0,0,1,0] => [[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,1,0,0,1,0,0] => [[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,1,0,0,0,0,1,0] => [[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,1,0,0,0,1,0,0] => [[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,0,1,1,0,0,1,0,0,0] => [[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,1,0,1,0,0,0,0] => [[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,0,0,0,1,0,1,0] => [[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,0,0,1,1,0,0] => [[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,0,1,0,0,1,0] => [[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,1,0,0,0,1,0] => [[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,1,0,0,1,0,0] => [[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,1,0,0,0,0,1,0] => [[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,1,1,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,1,0,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [.,[[[.,.],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [.,[[[.,.],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[[.,.],.]],.]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [.,[[.,.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [.,[[.,.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[.,[.,.]],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],.]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[.,[[[.,.],.],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [.,[[[.,.],.],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [.,[[[[.,[.,.]],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[.,[[.,.],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [[.,[[.,.],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [[.,[[.,.],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [[.,[[.,[.,.]],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [[.,[[[.,.],.],[.,[.,.]]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [[.,[[[.,.],.],[[.,.],.]]],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [[.,[[[[.,.],.],.],[.,.]]],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [[[[.,.],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [[[[.,.],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[[[.,.],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[[[.,[.,.]],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[[[.,.],.],[[.,.],.]],.],.] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1

[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[[.,.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [[[.,.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [[[.,.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [[[.,.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[[.,.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [[[.,.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [[[.,[.,.]],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [[[.,[.,.]],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [[[[.,.],.],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [[[[.,.],.],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[[[.,[.,.]],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[[[[.,.],.],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2

[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [[.,.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[.,.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[.,.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[.,[.,.]],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[.,[.,.]],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[[[.,.],.],.]]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[[.,.],.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[[.,[[.,.],.]],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,[[[.,[.,.]],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[[[[.,.],.],.],.]],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[[.,.],.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[[.,[.,.]],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[[.,[[.,[.,.]],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[[.,[[[.,.],.],.]],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[[[.,[[.,.],.]],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[[.,.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[[.,.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[.,.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[[.,[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[.,.],.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[[.,.],[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,.],[[.,.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[[.,[.,.]],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[.,.],.],[.,.]],[[.,.],.]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[[.,.],.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [[.,[.,[.,[.,.]]]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[.,[.,[[.,.],.]]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0] => [[.,[.,[.,[[.,[.,.]],.]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [[.,[.,[[.,.],.]]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [[.,[.,[[.,[.,[.,.]]],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [[.,[.,[[.,[[.,.],.]],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0] => [[.,[.,[[[.,[.,.]],.],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[[.,.],.],.],.]]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0] => [[.,[[.,[.,.]],.]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,.]]]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0] => [[.,[[.,[.,[[.,.],.]]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0] => [[.,[[.,[[.,[.,.]],.]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [[.,[[.,[[[.,.],.],.]],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [[.,[[[.,.],.],.]],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0] => [[.,[[[.,[.,[.,.]]],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [[.,[[[.,[[.,.],.]],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [[.,[[[[.,[.,.]],.],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[[[.,.],.],.],.],.]],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0] => [[[.,[.,[.,.]]],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [[[.,[[.,.],.]],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [[[.,[[.,[[.,.],.]],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0] => [[[[.,[.,.]],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [[[[.,[.,[[.,.],.]]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [[[[.,[[.,[.,.]],.]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [[[[[.,.],.],.],.],[[.,.],[.,.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[.,[[.,.],.]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[.,[[.,[.,.]],.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[.,[[[.,.],.],.]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[[.,[.,[.,.]]],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [[[.,.],[.,.]],[[[.,[.,.]],.],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[.,.],[.,.]],[[[[.,.],.],.],.]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,[.,[[[[[.,.],.],.],.],.]]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [[.,[[.,[.,[.,[.,[.,.]]]]],.]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[[[[.,.],.],.],.],.]],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0] => [[[[[[.,[[.,.],.]],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[.,.],[[[[.,[.,[.,[.,.]]]],.],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[.,.],[[[.,[.,[.,[.,[.,.]]]]],.],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[.,.],[.,[.,[.,[[[.,[.,.]],.],.]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

search for individual values

searching the database for the individual values of this statistic

Description

The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L.

Map

antichains of maximal size

Description

The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting

$A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$ , where

$\mathop{\downarrow} A$ is the order ideal generated by

$A$ .
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.

Map

to poset

Description

Return the poset obtained by interpreting the tree as a Hasse diagram.

Map

logarithmic height to pruning number

Description

Francon's map from Dyck paths to binary trees.
This bijection sends the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path., to the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree.. The implementation is a literal translation of Knuth's [2].