- FindStat

Identifier

Mp00013: Binary trees —to poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
Mp00197: Lattices —lattice of congruences⟶ Lattices
St001720: Lattices ⟶ ℤ

Values

[.,.] => ([],1) => ([],1) => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 450 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The minimal length of a chain of small intervals in a lattice.
An interval $[a, b]$ is small if $b$ is a join of elements covering $a$.

Map

lattice of congruences

Description

The lattice of congruences of a lattice.
A congruence of a lattice is an equivalence relation such that $a_1 \cong a_2$ and $b_1 \cong b_2$ implies $a_1 \vee b_1 \cong a_2 \vee b_2$ and $a_1 \wedge b_1 \cong a_2 \wedge b_2$.
The set of congruences ordered by refinement forms a lattice.

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.