Identifier
-
Mp00014:
Binary trees
—to 132-avoiding permutation⟶
Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000908: Posets ⟶ ℤ
Values
[.,[.,.]] => [2,1] => [1] => ([],1) => 1
[[.,.],.] => [1,2] => [1] => ([],1) => 1
[.,[.,[.,.]]] => [3,2,1] => [2,1] => ([],2) => 2
[.,[[.,.],.]] => [2,3,1] => [2,1] => ([],2) => 2
[[.,.],[.,.]] => [3,1,2] => [1,2] => ([(0,1)],2) => 1
[[.,[.,.]],.] => [2,1,3] => [2,1] => ([],2) => 2
[[[.,.],.],.] => [1,2,3] => [1,2] => ([(0,1)],2) => 1
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [3,2,1] => ([],3) => 3
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,2,1] => ([],3) => 3
[.,[[.,.],[.,.]]] => [4,2,3,1] => [2,3,1] => ([(1,2)],3) => 2
[.,[[.,[.,.]],.]] => [3,2,4,1] => [3,2,1] => ([],3) => 3
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,3,1] => ([(1,2)],3) => 2
[[.,.],[.,[.,.]]] => [4,3,1,2] => [3,1,2] => ([(1,2)],3) => 2
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,1,2] => ([(1,2)],3) => 2
[[.,[.,.]],[.,.]] => [4,2,1,3] => [2,1,3] => ([(0,2),(1,2)],3) => 1
[[[.,.],.],[.,.]] => [4,1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => [3,2,1] => ([],3) => 3
[[.,[[.,.],.]],.] => [2,3,1,4] => [2,3,1] => ([(1,2)],3) => 2
[[[.,.],[.,.]],.] => [3,1,2,4] => [3,1,2] => ([(1,2)],3) => 2
[[[.,[.,.]],.],.] => [2,1,3,4] => [2,1,3] => ([(0,2),(1,2)],3) => 1
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [4,3,2,1] => ([],4) => 4
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,3,2,1] => ([],4) => 4
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [3,4,2,1] => ([(2,3)],4) => 3
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [4,3,2,1] => ([],4) => 4
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,4,2,1] => ([(2,3)],4) => 3
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [4,2,3,1] => ([(2,3)],4) => 3
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [4,2,3,1] => ([(2,3)],4) => 3
[.,[[.,[.,.]],[.,.]]] => [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) => 4
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,4,2,1] => ([(2,3)],4) => 3
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [4,2,3,1] => ([(2,3)],4) => 3
[.,[[[.,[.,.]],.],.]] => [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) => 3
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [4,3,1,2] => ([(2,3)],4) => 3
[[.,.],[[.,.],[.,.]]] => [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) => 3
[[.,.],[[[.,.],.],.]] => [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) => 1
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 1
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 1
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [4,3,2,1] => ([],4) => 4
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [3,4,2,1] => ([(2,3)],4) => 3
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [4,2,3,1] => ([(2,3)],4) => 3
[[.,[[.,[.,.]],.]],.] => [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) => 3
[[[.,.],[[.,.],.]],.] => [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) => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [5,4,3,2,1] => ([],5) => 5
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,4,3,2,1] => ([],5) => 5
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 4
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [5,4,3,2,1] => ([],5) => 5
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 4
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 4
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 4
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 3
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 3
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [5,4,3,2,1] => ([],5) => 5
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,5,3,2,1] => ([(3,4)],5) => 4
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [5,3,4,2,1] => ([(3,4)],5) => 4
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 3
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 3
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 4
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 4
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 3
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [5,4,2,3,1] => ([(3,4)],5) => 4
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 3
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 3
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 3
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 3
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 3
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 2
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 2
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [5,4,3,2,1] => ([],5) => 5
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,5,3,2,1] => ([(3,4)],5) => 4
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [5,3,4,2,1] => ([(3,4)],5) => 4
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 3
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 3
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [5,4,2,3,1] => ([(3,4)],5) => 4
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 3
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 3
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 3
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 2
>>> Load all 818 entries. <<<[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 2
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 2
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 4
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 4
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 4
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 2
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 2
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [5,4,3,1,2] => ([(3,4)],5) => 4
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 3
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 2
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 2
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 3
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 3
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 2
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 3
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 2
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 3
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 3
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 2
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 3
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 2
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 2
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 2
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 2
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 2
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 2
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 2
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 1
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 1
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 1
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [5,4,3,2,1] => ([],5) => 5
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [4,5,3,2,1] => ([(3,4)],5) => 4
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [5,3,4,2,1] => ([(3,4)],5) => 4
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 3
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 3
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [5,4,2,3,1] => ([(3,4)],5) => 4
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 3
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 3
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 3
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 2
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 2
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5) => 2
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5) => 2
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [5,4,3,1,2] => ([(3,4)],5) => 4
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 3
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 3
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 2
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 2
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 3
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 2
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 3
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 2
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 2
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 2
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5) => 2
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => 2
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 1
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 1
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 1
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 6
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 6
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [6,5,4,3,2,1] => ([],6) => 6
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [6,5,4,3,2,1] => ([],6) => 6
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[[[.,.],[.,.]],.]]]] => [6,4,5,7,3,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4
[.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => [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) => 6
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[[.,[[[.,.],.],.]],.]]] => [4,5,6,3,7,2,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[.,[.,[[[.,.],[[.,.],.]],.]]] => [5,6,3,4,7,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[.,[.,[[[[.,.],.],[.,.]],.]]] => [6,3,4,5,7,2,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 4
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [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) => 5
[.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 5
[.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => [6,5,4,2,3,1] => ([(4,5)],6) => 5
[.,[[.,.],[.,[[[.,.],.],.]]]] => [5,6,7,4,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[[.,.],[[.,.],.]]]] => [6,7,4,5,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[[.,[.,.]],[.,.]]]] => [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) => 5
[.,[[.,.],[[.,[[.,.],.]],.]]] => [5,6,4,7,2,3,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[[[.,.],[.,.]],.]]] => [6,4,5,7,2,3,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,.],[[[.,[.,.]],.],.]]] => [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) => 4
[.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 4
[.,[[.,[.,.]],[[.,.],[.,.]]]] => [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) => 4
[.,[[.,[.,.]],[[[.,.],.],.]]] => [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) => 4
[.,[[[.,.],.],[.,[[.,.],.]]]] => [6,7,5,2,3,4,1] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 4
[.,[[[.,.],.],[[.,.],[.,.]]]] => [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) => 4
[.,[[[.,.],.],[[[.,.],.],.]]] => [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) => 2
[.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[.,[[.,[[[.,.],.],.]],[.,.]]] => [7,3,4,5,2,6,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[[.,.],[[.,.],.]],[.,.]]] => [7,4,5,2,3,6,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[.,[[[[.,.],.],[.,.]],[.,.]]] => [7,5,2,3,4,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[.,[[[.,[[.,.],.]],.],[.,.]]] => [7,3,4,2,5,6,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[.,[[[[.,.],[.,.]],.],[.,.]]] => [7,4,2,3,5,6,1] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [6,5,4,3,2,1] => ([],6) => 6
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4
[.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 4
[.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4
[.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 4
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [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) => 5
[.,[[[.,.],[.,[[.,.],.]]],.]] => [5,6,4,2,3,7,1] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[[.,.],[[.,.],[.,.]]],.]] => [6,4,5,2,3,7,1] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4
[.,[[[.,.],[[.,[.,.]],.]],.]] => [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) => 4
[.,[[[.,[.,.]],[[.,.],.]],.]] => [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) => 4
[.,[[[[.,.],.],[[.,.],.]],.]] => [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) => 2
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[.,[[[[.,.],[[.,.],.]],.],.]] => [4,5,2,3,6,7,1] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[.,[[[[[.,.],.],[.,.]],.],.]] => [5,2,3,4,6,7,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[.,[[[[[.,.],[.,.]],.],.],.]] => [4,2,3,5,6,7,1] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 5
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 5
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 5
[[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [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) => 5
[[.,.],[.,[[.,[[.,.],.]],.]]] => [5,6,4,7,3,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[[[.,.],[.,.]],.]]] => [6,4,5,7,3,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[.,[[[.,[.,.]],.],.]]] => [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) => 4
[[.,.],[[.,.],[.,[[.,.],.]]]] => [6,7,5,3,4,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[[.,.],[[.,.],[.,.]]]] => [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) => 4
[[.,.],[[.,.],[[[.,.],.],.]]] => [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) => 2
[[.,.],[[.,[[.,.],.]],[.,.]]] => [7,4,5,3,6,1,2] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[.,.],[[[.,.],[.,.]],[.,.]]] => [7,5,3,4,6,1,2] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 2
[[.,.],[[[[.,.],.],.],[.,.]]] => [7,3,4,5,6,1,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => [6,5,4,3,1,2] => ([(4,5)],6) => 5
[[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4
[[.,.],[[.,[[.,[.,.]],.]],.]] => [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) => 4
[[.,.],[[[.,.],[[.,.],.]],.]] => [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) => 2
[[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[.,.],[[[[.,.],[.,.]],.],.]] => [5,3,4,6,7,1,2] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 2
[[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 4
[[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 4
[[.,[.,.]],[.,[[.,.],[.,.]]]] => [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) => 4
[[.,[.,.]],[.,[[[.,.],.],.]]] => [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) => 2
[[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2
[[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 4
[[.,[.,.]],[[.,[[.,.],.]],.]] => [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) => 2
[[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 4
[[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 4
[[[.,.],.],[.,[[.,.],[.,.]]]] => [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) => 4
[[[.,.],.],[.,[[[.,.],.],.]]] => [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) => 2
[[[.,.],.],[[[.,.],.],[.,.]]] => [7,4,5,6,1,2,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2
[[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 4
[[[.,.],.],[[.,[[.,.],.]],.]] => [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) => 2
[[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [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) => 2
[[.,[.,[.,.]]],[[.,[.,.]],.]] => [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) => 2
[[.,[[.,.],.]],[.,[.,[.,.]]]] => [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) => 2
[[.,[[.,.],.]],[[.,[.,.]],.]] => [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) => 2
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [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) => 2
[[[.,.],[.,.]],[[.,[.,.]],.]] => [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) => 2
[[[.,[.,.]],.],[.,[.,[.,.]]]] => [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) => 2
[[[.,[.,.]],.],[[.,[.,.]],.]] => [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) => 2
[[[[.,.],.],.],[.,[.,[.,.]]]] => [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) => 2
[[[[.,.],.],.],[[.,[.,.]],.]] => [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) => 2
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[.,[[[.,.],.],.]],[.,[.,.]]] => [7,6,2,3,4,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[.,[[[.,.],.],.]],[[.,.],.]] => [6,7,2,3,4,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[.,.],[[.,.],.]],[.,[.,.]]] => [7,6,3,4,1,2,5] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[.,.],[[.,.],.]],[[.,.],.]] => [6,7,3,4,1,2,5] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[[.,.],.],[.,.]],[.,[.,.]]] => [7,6,4,1,2,3,5] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[.,.],.],[.,.]],[[.,.],.]] => [6,7,4,1,2,3,5] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[[[.,[[.,.],.]],.],[.,[.,.]]] => [7,6,2,3,1,4,5] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[.,[[.,.],.]],.],[[.,.],.]] => [6,7,2,3,1,4,5] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[[.,.],[.,.]],.],[.,[.,.]]] => [7,6,3,1,2,4,5] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[[.,.],[.,.]],.],[[.,.],.]] => [6,7,3,1,2,4,5] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 1
[[.,[[.,[[.,.],.]],.]],[.,.]] => [7,3,4,2,5,1,6] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[.,[[[.,.],[.,.]],.]],[.,.]] => [7,4,2,3,5,1,6] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1
[[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,.],[.,[[.,.],.]]],[.,.]] => [7,4,5,3,1,2,6] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,.],[[.,.],[.,.]]],[.,.]] => [7,5,3,4,1,2,6] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,.],[[[.,.],.],.]],[.,.]] => [7,3,4,5,1,2,6] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1
[[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[.,.],.],[[.,.],.]],[.,.]] => [7,4,5,1,2,3,6] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1
[[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 1
[[[.,[[.,.],.]],[.,.]],[.,.]] => [7,5,2,3,1,4,6] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[[.,.],[.,.]],[.,.]],[.,.]] => [7,5,3,1,2,4,6] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1
[[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 1
[[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 1
[[[.,[[[.,.],.],.]],.],[.,.]] => [7,2,3,4,1,5,6] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[[.,.],[[.,.],.]],.],[.,.]] => [7,3,4,1,2,5,6] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
[[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 1
[[[[[.,.],.],[.,.]],.],[.,.]] => [7,4,1,2,3,5,6] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 1
[[[[.,[[.,.],.]],.],.],[.,.]] => [7,2,3,1,4,5,6] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[[[[[.,.],[.,.]],.],.],[.,.]] => [7,3,1,2,4,5,6] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
[[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1] => ([],6) => 6
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [5,6,4,3,2,1] => ([(4,5)],6) => 5
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => [6,4,5,3,2,1] => ([(4,5)],6) => 5
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 4
[[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 4
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1] => ([(4,5)],6) => 5
[[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 4
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 4
[[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 4
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [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) => 5
[[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 4
[[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 4
[[.,[[.,.],[[.,[.,.]],.]]],.] => [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) => 4
[[.,[[.,[.,.]],[[.,.],.]]],.] => [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) => 4
[[.,[[[.,.],.],[[.,.],.]]],.] => [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) => 2
[[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [6,5,4,3,1,2] => ([(4,5)],6) => 5
[[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 4
[[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 4
[[[.,.],[.,[[.,[.,.]],.]]],.] => [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) => 4
[[[.,.],[[.,.],[[.,.],.]]],.] => [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) => 2
[[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 2
[[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 2
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 2
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 4
[[[.,[.,.]],[.,[[.,.],.]]],.] => [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) => 2
[[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 2
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 4
[[[[.,.],.],[.,[[.,.],.]]],.] => [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) => 2
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 2
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [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) => 2
[[[.,[[.,.],.]],[.,[.,.]]],.] => [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) => 2
[[[[.,.],[.,.]],[.,[.,.]]],.] => [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) => 2
[[[[.,[.,.]],.],[.,[.,.]]],.] => [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) => 2
[[[[[.,.],.],.],[.,[.,.]]],.] => [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) => 2
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 2
[[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 2
[[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 2
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 2
[[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 2
[[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 2
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 2
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 2
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => [3,4,2,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => [4,2,3,5,1,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => [3,2,4,5,1,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1
[[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 1
[[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[.,.],[[[.,.],.],.]],.],.] => [3,4,5,1,2,6,7] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1
[[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 1
[[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 1
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 1
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 1
[[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 1
[[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => [5,2,3,1,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [5,3,1,2,4,6] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => 1
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [5,2,1,3,4,6] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => 1
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 1
[[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [2,3,4,1,5,6,7] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 1
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 1
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 1
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [7,5,6,8,4,3,2,1] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 5
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 5
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] => [8,7,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => 5
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]] => [6,5,7,4,8,3,2,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 5
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [7,6,4,5,8,3,2,1] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 6
[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [7,5,4,6,8,3,2,1] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => 5
[.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [7,4,5,6,8,3,2,1] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 5
[.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => 4
[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 6
[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 6
[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => 5
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 5
[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]] => [8,7,5,4,3,6,2,1] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 4
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]] => [5,4,6,7,3,8,2,1] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => 4
[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [7,6,5,3,4,8,2,1] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 6
[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [7,6,4,3,5,8,2,1] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 5
[.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [7,6,3,4,5,8,2,1] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 5
[.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 3
[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 6
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 6
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 5
[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => 5
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 5
[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,2,4,1] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 5
[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3
[.,[[.,[.,.]],[[[[.,.],.],.],.]]] => [5,6,7,8,3,2,4,1] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,2,3,4,1] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 5
[.,[[[[.,[.,.]],.],.],[[.,.],.]]] => [7,8,3,2,4,5,6,1] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 3
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1] => [7,6,5,4,3,2,1] => ([],7) => 7
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 6
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]] => [6,5,7,4,3,2,8,1] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 5
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]] => [6,5,4,3,7,2,8,1] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]] => [5,4,6,3,7,2,8,1] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 3
[.,[[.,[[[.,.],[.,[.,.]]],.]],.]] => [6,5,3,4,7,2,8,1] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 3
[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,2,3,8,1] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 6
[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [7,6,5,3,2,4,8,1] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 5
[.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [7,6,5,2,3,4,8,1] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 5
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [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) => 2
[.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [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) => 2
[.,[[[[[[.,[.,.]],.],.],.],.],.]] => [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) => 2
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 6
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 6
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 4
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => [7,6,5,8,3,4,1,2] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 5
[[.,.],[[.,.],[[[.,[.,.]],.],.]]] => [6,5,7,8,3,4,1,2] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 3
[[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => [7,8,5,4,3,6,1,2] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 3
[[.,.],[[[.,[.,.]],.],[[.,.],.]]] => [7,8,4,3,5,6,1,2] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 3
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [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) => 2
[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 6
[[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 4
[[.,.],[[.,[[[.,[.,.]],.],.]],.]] => [5,4,6,7,3,8,1,2] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 3
[[.,.],[[[.,[[.,[.,.]],.]],.],.]] => [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) => 2
[[.,.],[[[[.,[.,.]],[.,.]],.],.]] => [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) => 2
[[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [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) => 2
[[.,.],[[[[[.,[.,.]],.],.],.],.]] => [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) => 2
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,2,1,3] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 5
[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 5
[[.,[.,.]],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,2,1,3] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[[.,[.,.]],[[[[[.,.],.],.],.],.]] => [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) => 2
[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 5
[[[.,.],.],[.,[[[.,[.,.]],.],.]]] => [6,5,7,8,4,1,2,3] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [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) => 2
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]] => [8,7,6,5,3,2,1,4] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 4
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]] => [7,8,5,6,3,2,1,4] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 3
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 4
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [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) => 2
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 4
[[[.,[.,.]],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,2,1,3,4] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 4
[[[.,[.,.]],.],[.,[[[.,.],.],.]]] => [6,7,8,5,2,1,3,4] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 3
[[[.,[.,.]],.],[[.,.],[[.,.],.]]] => [7,8,5,6,2,1,3,4] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 3
[[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [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) => 2
[[[.,[.,.]],.],[[[[.,.],.],.],.]] => [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) => 2
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 4
[[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 4
[[[[.,.],.],.],[.,[[.,[.,.]],.]]] => [7,6,8,5,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 4
[[[[.,.],.],.],[[.,[.,.]],[.,.]]] => [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) => 2
[[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 4
[[[[.,.],.],.],[[[.,[.,.]],.],.]] => [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) => 2
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]] => [8,7,6,4,3,2,1,5] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]] => [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) => 2
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]] => [8,7,6,3,4,2,1,5] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 3
[[.,[.,[[.,.],.]]],[[[.,.],.],.]] => [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) => 2
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,2,3,1,5] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 3
[[.,[[.,.],[.,.]]],[[[.,.],.],.]] => [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) => 2
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]] => [8,7,6,3,2,4,1,5] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 3
[[.,[[.,[.,.]],.]],[[[.,.],.],.]] => [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) => 2
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]] => [8,7,6,4,3,1,2,5] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 3
[[[.,.],[.,[.,.]]],[[[.,.],.],.]] => [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) => 2
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]] => [8,7,6,4,2,1,3,5] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 3
[[[.,[.,.]],[.,.]],[[[.,.],.],.]] => [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) => 2
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]] => [8,7,6,3,2,1,4,5] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => 3
[[[.,[.,[.,.]]],.],[[[.,.],.],.]] => [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) => 2
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]] => [8,7,6,2,1,3,4,5] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => 3
[[[[.,[.,.]],.],.],[[[.,.],.],.]] => [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) => 2
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]] => [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) => 2
[[[.,[.,.]],[.,[.,.]]],[[.,.],.]] => [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) => 2
[[[[.,.],.],[.,[.,.]]],[[.,.],.]] => [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) => 2
[[[[.,[.,.]],.],[.,.]],[.,[.,.]]] => [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) => 2
[[[[.,[.,.]],.],[.,.]],[[.,.],.]] => [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) => 2
[[[[[.,.],.],.],[.,.]],[.,[.,.]]] => [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) => 2
[[[[[.,.],.],.],[.,.]],[[.,.],.]] => [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) => 2
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]] => [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) => 2
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]] => [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) => 2
[[[.,[[.,[.,.]],.]],.],[[.,.],.]] => [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) => 2
[[[[.,[.,.]],[.,.]],.],[[.,.],.]] => [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) => 2
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]] => [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) => 2
[[[[.,[.,[.,.]]],.],.],[[.,.],.]] => [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) => 2
[[[[[.,[.,.]],.],.],.],[[.,.],.]] => [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) => 2
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]] => [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) => 1
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]] => [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) => 1
[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]] => [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) => 1
[[[.,.],[[[.,[.,.]],.],.]],[.,.]] => [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) => 1
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]] => [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) => 1
[[[.,[[.,.],.]],[.,[.,.]]],[.,.]] => [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) => 1
[[[[.,[.,.]],.],[[.,.],.]],[.,.]] => [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) => 1
[[[[[.,.],.],.],[.,[.,.]]],[.,.]] => [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) => 1
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [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) => 1
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]] => [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) => 1
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]] => [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) => 1
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]] => [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) => 1
[[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [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) => 1
[[[[[[.,[.,.]],.],.],.],.],[.,.]] => [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) => 1
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [7,6,5,4,3,2,1] => ([],7) => 7
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.] => [6,7,5,4,3,2,1,8] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 6
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.] => [6,5,7,4,3,2,1,8] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 5
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.] => [5,6,7,4,3,2,1,8] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 5
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.] => [7,6,4,5,3,2,1,8] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 6
[[.,[.,[.,[[[.,.],.],[.,.]]]]],.] => [7,4,5,6,3,2,1,8] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 5
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.] => [6,5,4,7,3,2,1,8] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 4
[[.,[.,[[.,.],[[.,.],[.,.]]]]],.] => [7,5,6,3,4,2,1,8] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 5
[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.] => [7,6,4,3,5,2,1,8] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 5
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.] => [7,6,3,4,5,2,1,8] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 5
[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.] => [7,5,4,3,6,2,1,8] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 4
[[.,[[.,.],[.,[.,[[.,.],.]]]]],.] => [6,7,5,4,2,3,1,8] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 5
[[.,[[.,.],[[.,.],[.,[.,.]]]]],.] => [7,6,4,5,2,3,1,8] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 5
[[.,[[.,[.,.]],[[.,[.,.]],.]]],.] => [6,5,7,3,2,4,1,8] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3
[[.,[[.,[.,.]],[[[.,.],.],.]]],.] => [5,6,7,3,2,4,1,8] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[[.,[[[.,.],.],[.,[.,[.,.]]]]],.] => [7,6,5,2,3,4,1,8] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 5
[[.,[[[.,.],.],[[.,[.,.]],.]]],.] => [6,5,7,2,3,4,1,8] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[[.,[[[.,[.,[.,[.,.]]]],.],.]],.] => [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) => 2
[[.,[[[[[.,[.,.]],.],.],.],.]],.] => [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) => 2
[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [7,6,5,4,3,1,2,8] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 6
[[[.,.],[.,[.,[[.,.],[.,.]]]]],.] => [7,5,6,4,3,1,2,8] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 5
[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,2,1,3,8] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 5
[[[.,[.,.]],[.,[[.,[.,.]],.]]],.] => [6,5,7,4,2,1,3,8] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3
[[[.,[.,.]],[[.,[.,.]],[.,.]]],.] => [7,5,4,6,2,1,3,8] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 3
[[[.,[.,.]],[[[.,.],.],[.,.]]],.] => [7,4,5,6,2,1,3,8] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 3
[[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [7,6,5,4,1,2,3,8] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 5
[[[[.,.],.],[[[.,[.,.]],.],.]],.] => [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) => 2
[[[[.,[.,.]],.],[[[.,.],.],.]],.] => [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) => 2
[[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [7,6,5,1,2,3,4,8] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 4
[[[[[.,.],.],.],[[.,[.,.]],.]],.] => [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) => 2
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [7,6,4,3,2,1,5,8] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 3
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.] => [7,6,4,3,1,2,5,8] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 3
[[[[[[.,.],.],.],[.,.]],[.,.]],.] => [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) => 2
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [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) => 2
[[[[[[.,[.,.]],.],.],.],[.,.]],.] => [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) => 2
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [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) => 1
[[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [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) => 1
[[[.,[[.,[.,[[.,.],.]]],.]],.],.] => [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) => 1
[[[.,[[[[.,.],[.,.]],.],.]],.],.] => [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) => 1
[[[[.,.],[.,[.,[[.,.],.]]]],.],.] => [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) => 1
[[[[.,.],[.,[[.,[.,.]],.]]],.],.] => [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) => 1
[[[[.,.],[[.,[.,[.,.]]],.]],.],.] => [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) => 1
[[[[.,[.,.]],[.,[[.,.],.]]],.],.] => [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) => 1
[[[[.,[.,.]],[[.,[.,.]],.]],.],.] => [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) => 1
[[[[.,[.,[.,.]]],[[.,.],.]],.],.] => [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) => 1
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.] => [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) => 1
[[[[[.,.],[.,[.,.]]],[.,.]],.],.] => [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) => 1
[[[[[.,[[.,.],.]],.],[.,.]],.],.] => [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) => 1
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [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) => 1
[[[[.,[[[.,.],.],[.,.]]],.],.],.] => [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) => 1
[[[[.,[[[[.,.],.],.],.]],.],.],.] => [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) => 1
[[[[[[[.,.],.],.],[.,.]],.],.],.] => [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) => 1
[[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [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) => 1
[[[[[.,[[.,[.,.]],.]],.],.],.],.] => [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) => 1
[[[[[[.,[.,[.,.]]],.],.],.],.],.] => [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) => 1
[[[[[[[.,[.,.]],.],.],.],.],.],.] => [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) => 1
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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:
2,3 4,6,4 10,15,12,5 28,42,36,20,6 84,126,112,70,30,7
$F_{2} = 2\ q$
$F_{3} = 2\ q + 3\ q^{2}$
$F_{4} = 4\ q + 6\ q^{2} + 4\ q^{3}$
$F_{5} = 10\ q + 15\ q^{2} + 12\ q^{3} + 5\ q^{4}$
$F_{6} = 28\ q + 42\ q^{2} + 36\ q^{3} + 20\ q^{4} + 6\ q^{5}$
$F_{7} = 84\ q + 126\ q^{2} + 112\ q^{3} + 70\ q^{4} + 30\ q^{5} + 7\ q^{6}$
Description
The length of the shortest maximal antichain in a poset.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
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
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.
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