Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001300: Posets ⟶ ℤ
Values
[.,[.,.]] => [2,1] => [1] => ([],1) => 0
[[.,.],.] => [1,2] => [1] => ([],1) => 0
[.,[.,[.,.]]] => [3,2,1] => [2,1] => ([],2) => 0
[.,[[.,.],.]] => [2,3,1] => [2,1] => ([],2) => 0
[[.,.],[.,.]] => [3,1,2] => [1,2] => ([(0,1)],2) => 1
[[.,[.,.]],.] => [2,1,3] => [2,1] => ([],2) => 0
[[[.,.],.],.] => [1,2,3] => [1,2] => ([(0,1)],2) => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,2,1] => ([],3) => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,2,1] => ([],3) => 0
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,3,1] => ([(1,2)],3) => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,1] => ([],3) => 0
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,1] => ([(1,2)],3) => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => [3,1,2] => ([(1,2)],3) => 1
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,1,2] => ([(1,2)],3) => 1
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,1,3] => ([(0,2),(1,2)],3) => 2
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1] => ([],3) => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1] => ([(1,2)],3) => 1
[[[.,.],[.,.]],.] => [3,1,2,4] => [3,1,2] => ([(1,2)],3) => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3) => 2
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3) => 2
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [4,3,2,1] => ([],4) => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,3,2,1] => ([],4) => 0
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,4,2,1] => ([(2,3)],4) => 1
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,2,1] => ([],4) => 0
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,2,1] => ([(2,3)],4) => 1
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [4,2,3,1] => ([(2,3)],4) => 1
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [4,2,3,1] => ([(2,3)],4) => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [3,2,4,1] => ([(1,3),(2,3)],4) => 2
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [2,3,4,1] => ([(1,2),(2,3)],4) => 2
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [4,3,2,1] => ([],4) => 0
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,1] => ([(2,3)],4) => 1
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [4,2,3,1] => ([(2,3)],4) => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [3,2,4,1] => ([(1,3),(2,3)],4) => 2
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,3,4,1] => ([(1,2),(2,3)],4) => 2
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [4,3,1,2] => ([(2,3)],4) => 1
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [4,3,1,2] => ([(2,3)],4) => 1
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [3,4,1,2] => ([(0,3),(1,2)],4) => 2
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [4,3,1,2] => ([(2,3)],4) => 1
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,4,1,2] => ([(0,3),(1,2)],4) => 2
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4) => 2
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [4,2,1,3] => ([(1,3),(2,3)],4) => 2
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4) => 2
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [4,1,2,3] => ([(1,2),(2,3)],4) => 2
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 3
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 3
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 3
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 3
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1] => ([],4) => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1] => ([(2,3)],4) => 1
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [4,2,3,1] => ([(2,3)],4) => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [3,2,4,1] => ([(1,3),(2,3)],4) => 2
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [2,3,4,1] => ([(1,2),(2,3)],4) => 2
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [4,3,1,2] => ([(2,3)],4) => 1
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [3,4,1,2] => ([(0,3),(1,2)],4) => 2
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [4,2,1,3] => ([(1,3),(2,3)],4) => 2
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [4,1,2,3] => ([(1,2),(2,3)],4) => 2
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 3
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 3
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 3
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 3
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 3
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [5,4,3,2,1] => ([],5) => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,4,3,2,1] => ([],5) => 0
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 1
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,3,2,1] => ([],5) => 0
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 1
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 2
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,2,1] => ([],5) => 0
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 1
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 2
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 1
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 1
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 2
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 1
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 2
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 2
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 2
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 3
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 3
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 3
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,1] => ([],5) => 0
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,1] => ([(3,4)],5) => 1
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [5,3,4,2,1] => ([(3,4)],5) => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 2
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 2
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [5,4,2,3,1] => ([(3,4)],5) => 1
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 2
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 2
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 2
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 3
>>> Load all 818 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 3
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 3
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 1
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 1
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 1
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 3
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 3
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 1
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 2
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 3
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 3
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 2
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 2
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 3
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 2
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 3
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 2
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 2
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 3
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 2
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 3
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 3
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 3
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 3
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 3
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 4
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 4
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 4
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 4
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 4
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 4
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 4
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 4
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 4
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1] => ([],5) => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1] => ([(3,4)],5) => 1
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [5,3,4,2,1] => ([(3,4)],5) => 1
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 2
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [5,4,2,3,1] => ([(3,4)],5) => 1
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 2
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 2
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 2
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 3
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 3
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 3
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 3
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [5,4,3,1,2] => ([(3,4)],5) => 1
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 2
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 2
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 3
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 3
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 2
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 3
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 2
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 3
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 3
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 3
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 3
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 3
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 4
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 4
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 4
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 4
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 4
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 4
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 4
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 4
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 4
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 4
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 4
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 4
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 2
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 2
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[.,[[.,[[.,.],.]],[.,.]]]] => [7,4,5,3,6,2,1] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[.,[[[.,.],[.,.]],[.,.]]]] => [7,5,3,4,6,2,1] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 2
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 2
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[.,[[[[.,.],[.,.]],.],.]]] => [5,3,4,6,7,2,1] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[.,.],[[[.,.],.],[.,.]]]] => [7,4,5,6,2,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[.,.],[[[[.,.],.],.],.]]] => [4,5,6,7,2,3,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 2
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 2
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 2
[.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 2
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 2
[.,[[[.,.],.],[[.,.],[.,.]]]] => [7,5,6,2,3,4,1] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 2
[.,[[[.,.],.],[[[.,.],.],.]]] => [5,6,7,2,3,4,1] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[[.,.],.]],[.,[.,.]]]] => [7,6,3,4,2,5,1] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[.,[[.,.],.]],[[.,.],.]]] => [6,7,3,4,2,5,1] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[[.,.],[.,.]],[.,[.,.]]]] => [7,6,4,2,3,5,1] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[[.,.],[.,.]],[[.,.],.]]] => [6,7,4,2,3,5,1] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[[[[.,.],.],.],[[.,.],.]]] => [6,7,2,3,4,5,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,1] => ([],6) => 0
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 2
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 2
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 2
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 2
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 2
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[.,[[.,[[.,.],.]],.]],.]] => [4,5,3,6,2,7,1] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[.,[[[.,.],[.,.]],.]],.]] => [5,3,4,6,2,7,1] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 2
[.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[[.,.],[[[.,.],.],.]],.]] => [4,5,6,2,3,7,1] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 2
[.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 3
[.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 2
[.,[[[[.,.],.],[[.,.],.]],.]] => [5,6,2,3,4,7,1] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 3
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 3
[.,[[[.,[[.,.],.]],[.,.]],.]] => [6,3,4,2,5,7,1] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[[[.,.],[.,.]],[.,.]],.]] => [6,4,2,3,5,7,1] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 3
[.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 3
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[.,.],[[.,.],[.,.]]]] => [7,5,6,3,4,1,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 3
[[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[.,.],[[[.,.],.],.]]] => [5,6,7,3,4,1,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 3
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[[[.,.],.],[.,[.,.]]]] => [7,6,3,4,5,1,2] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[[[.,.],.],[[.,.],.]]] => [6,7,3,4,5,1,2] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 2
[[.,.],[[[.,.],[[.,.],.]],.]] => [5,6,3,4,7,1,2] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 3
[[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,.],[[[[.,.],.],[.,.]],.]] => [6,3,4,5,7,1,2] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 2
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 2
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 2
[[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 2
[[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 2
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 2
[[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 2
[[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[[.,.],[.,[.,.]]]] => [7,6,4,5,1,2,3] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[[.,.],[[.,.],.]]] => [6,7,4,5,1,2,3] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 4
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 2
[[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[[[.,.],[.,.]],.]] => [6,4,5,7,1,2,3] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 4
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 3
[[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 3
[[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 3
[[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [7,6,5,2,3,1,4] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[[.,.],.]],[.,[[.,.],.]]] => [6,7,5,2,3,1,4] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[[.,.],.]],[[.,.],[.,.]]] => [7,5,6,2,3,1,4] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[[.,.],.]],[[[.,.],.],.]] => [5,6,7,2,3,1,4] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [7,6,5,3,1,2,4] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[[.,.],[.,.]],[.,[[.,.],.]]] => [6,7,5,3,1,2,4] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[[.,.],[.,.]],[[.,.],[.,.]]] => [7,5,6,3,1,2,4] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[[.,.],[.,.]],[[[.,.],.],.]] => [5,6,7,3,1,2,4] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 3
[[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 3
[[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 3
[[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 3
[[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 3
[[[[.,.],.],.],[[.,.],[.,.]]] => [7,5,6,1,2,3,4] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 3
[[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 5
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 5
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 5
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 5
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 5
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 5
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 5
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 5
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 5
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 5
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 5
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 5
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 5
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 5
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 5
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 5
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 5
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 5
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => ([],6) => 0
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => ([(4,5)],6) => 1
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [6,4,5,3,2,1] => ([(4,5)],6) => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 2
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1] => ([(4,5)],6) => 1
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 2
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 2
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 3
[[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 3
[[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 3
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => [6,5,4,2,3,1] => ([(4,5)],6) => 1
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 2
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 2
[[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 2
[[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 3
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 2
[[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 3
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 3
[[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 3
[[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 3
[[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 3
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2] => ([(4,5)],6) => 1
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 2
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 2
[[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 2
[[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 3
[[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 3
[[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 3
[[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 2
[[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 3
[[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 4
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 2
[[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 3
[[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 4
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 4
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 3
[[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 4
[[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 3
[[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 4
[[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 3
[[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 4
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 3
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 4
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 4
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 4
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 4
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 4
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 4
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 4
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 4
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 4
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 4
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 5
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 5
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 5
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 5
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 5
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 5
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 5
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 5
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 5
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 5
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 5
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 5
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 5
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 5
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 5
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 5
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 5
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 5
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 5
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 5
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 5
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 5
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 5
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 5
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 5
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 2
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 2
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => 2
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 2
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 1
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => 2
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 2
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => 3
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 1
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 1
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => 2
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 2
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 3
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => 3
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 1
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 2
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 2
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 4
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 1
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 1
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 2
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => 2
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 2
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 2
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 4
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 2
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 4
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,1] => ([],7) => 0
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 1
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 2
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 4
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 4
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 1
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 2
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 2
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 5
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 5
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 1
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 1
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 3
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 2
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 4
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 4
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 4
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 5
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 1
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 3
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 4
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [5,4,6,3,7,8,1,2] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 5
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [6,4,3,5,7,8,1,2] => [6,4,3,5,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 5
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2] => [5,4,3,6,7,1,2] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 5
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 5
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 2
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 2
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,2,1,3] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 5
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 2
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 5
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 3
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 4
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 3
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [5,6,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 5
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 3
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 3
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 4
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 4
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => [6,5,7,2,1,3,4] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 5
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [5,6,7,8,2,1,3,4] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 5
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 3
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 3
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 3
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [8,6,5,7,1,2,3,4] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 5
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 3
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 5
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [6,7,8,4,3,2,1,5] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 5
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 4
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [6,7,8,3,4,2,1,5] => [6,7,3,4,2,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 5
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 4
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [6,7,8,4,2,3,1,5] => [6,7,4,2,3,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 5
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 4
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [6,7,8,3,2,4,1,5] => [6,7,3,2,4,1,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 5
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 4
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [6,7,8,4,3,1,2,5] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 5
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 4
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [6,7,8,4,2,1,3,5] => [6,7,4,2,1,3,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 5
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => 4
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [6,7,8,3,2,1,4,5] => [6,7,3,2,1,4,5] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 5
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => 4
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [6,7,8,2,1,3,4,5] => [6,7,2,1,3,4,5] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 5
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [7,8,5,4,3,2,1,6] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,2,1,3,6] => [7,5,4,2,1,3,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 5
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [7,8,5,4,1,2,3,6] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 5
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [8,7,5,2,1,3,4,6] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 5
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [7,8,5,2,1,3,4,6] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 5
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [8,7,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 5
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [7,8,5,1,2,3,4,6] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 5
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [8,7,4,3,2,1,5,6] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [7,8,4,3,2,1,5,6] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [7,8,3,2,4,1,5,6] => [7,3,2,4,1,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 5
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [7,8,4,2,1,3,5,6] => [7,4,2,1,3,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 5
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [8,7,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 5
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [7,8,3,2,1,4,5,6] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 5
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [7,8,2,1,3,4,5,6] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 5
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [8,6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [8,4,5,6,3,2,1,7] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 6
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [8,6,5,4,3,1,2,7] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 6
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [8,4,3,5,6,1,2,7] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 6
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [8,6,5,4,2,1,3,7] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 6
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [8,6,5,2,3,1,4,7] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 6
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [8,5,6,2,1,3,4,7] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 6
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [8,6,5,1,2,3,4,7] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 6
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 6
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [8,6,3,4,2,1,5,7] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 6
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [8,6,4,2,1,3,5,7] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 6
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [8,4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 6
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [8,3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 6
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [8,2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 6
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => ([],7) => 0
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 1
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 2
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 2
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 1
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 2
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 3
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 2
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 2
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 2
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 3
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 2
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 2
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 4
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 2
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [5,4,3,2,6,7,1,8] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [3,2,4,5,6,7,1,8] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 5
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 1
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 2
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 2
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 4
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 4
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 4
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 2
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [5,4,6,7,1,2,3,8] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 5
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [5,6,7,2,1,3,4,8] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 5
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 3
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [6,5,7,1,2,3,4,8] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 5
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 4
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 4
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [7,5,1,2,3,4,6,8] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 5
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [7,4,3,2,1,5,6,8] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 5
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [7,2,1,3,4,5,6,8] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 5
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 6
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 6
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [4,5,3,2,6,1,7,8] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 6
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [4,2,3,5,6,1,7,8] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 6
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [5,6,4,3,1,2,7,8] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 6
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [5,4,6,3,1,2,7,8] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 6
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [5,4,3,6,1,2,7,8] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 6
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [5,6,4,2,1,3,7,8] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 6
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [5,4,6,2,1,3,7,8] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 6
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [5,6,3,2,1,4,7,8] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 6
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [6,4,3,2,1,5,7,8] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 6
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [6,4,3,1,2,5,7,8] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 6
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [6,2,3,1,4,5,7,8] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 6
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 6
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [5,2,3,4,1,6,7,8] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 6
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [2,3,4,5,1,6,7,8] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 6
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 6
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 6
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [3,2,4,1,5,6,7,8] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 6
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 6
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
3,2 4,6,4 5,12,15,10 6,20,36,42,28 7,30,70,112,126,84
$F_{2} = 2$
$F_{3} = 3 + 2\ q$
$F_{4} = 4 + 6\ q + 4\ q^{2}$
$F_{5} = 5 + 12\ q + 15\ q^{2} + 10\ q^{3}$
$F_{6} = 6 + 20\ q + 36\ q^{2} + 42\ q^{3} + 28\ q^{4}$
$F_{7} = 7 + 30\ q + 70\ q^{2} + 112\ q^{3} + 126\ q^{4} + 84\ q^{5}$
Description
The rank of the boundary operator in degree 1 of the chain complex of the order complex of the poset.
Map
restriction
Description
The permutation obtained by removing the largest letter.
This map is undefined for the empty permutation.
This map is undefined for the empty permutation.
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.
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.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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