- FindStat

Identifier

Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00074: Posets —to graph⟶ Graphs
St001120: Graphs ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 625 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 2\ q + 2\ q^{2}$

$F_{4} = 1 + 4\ q + 6\ q^{2} + 3\ q^{3}$

$F_{5} = 1 + 7\ q + 16\ q^{2} + 14\ q^{3} + 4\ q^{4}$

$F_{6} = 1 + 12\ q + 40\ q^{2} + 46\ q^{3} + 28\ q^{4} + 5\ q^{5}$

$F_{7} = 1 + 20\ q + 96\ q^{2} + 136\ q^{3} + 124\ q^{4} + 46\ q^{5} + 6\ q^{6}$

Description

The length of a longest path in a graph.

Map

to graph

Description

Returns the Hasse diagram of the poset as an undirected graph.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$
and the cover relation is given by

$(w, x) \leq (y, z)$ if

$w \leq y$ and

$x \leq z$ .
For example, the permutation

$[3,1,5,4,2]$ is mapped to the poset with cover relations

$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$

Map

to 132-avoiding permutation

Description

Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.