- FindStat

Identifier

Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001301: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 474 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 5$

$F_{4} = 14$

$F_{5} = 42$

$F_{6} = 132$

Description

The first Betti number of the order complex associated with the poset.
The order complex of a poset is the simplicial complex whose faces are the chains of the poset. This statistic is the rank of the first homology group of the order complex.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

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

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

$w \leq y$ and

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

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

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

Map

left-right symmetry

Description

Return the left-right symmetrized tree of a binary tree.

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.