- FindStat

Identifier

Mp00013: Binary trees —to poset⟶ Posets
Mp00110: Posets —Greene-Kleitman invariant⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001190: Dyck paths ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 386 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = q^{3}$

$F_{2} = 2\ q^{4}$

$F_{3} = q^{4} + 4\ q^{5}$

$F_{4} = 6\ q^{5} + 8\ q^{6}$

$F_{5} = 6\ q^{5} + 20\ q^{6} + 16\ q^{7}$

Description

Number of simple modules with projective dimension at most 4 in the corresponding Nakayama algebra.

Map

to Dyck path

Description

Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.

Map

Greene-Kleitman invariant

Description

The Greene-Kleitman invariant of a poset.
This is the partition

$(c_1 - c_0, c_2 - c_1, c_3 - c_2, \ldots)$ , where

$c_k$ is the maximum cardinality of a union of

$k$ chains of the poset. Equivalently, this is the conjugate of the partition

$(a_1 - a_0, a_2 - a_1, a_3 - a_2, \ldots)$ , where

$a_k$ is the maximum cardinality of a union of

$k$ antichains of the poset.

Map

to poset

Description

Return the poset obtained by interpreting the tree as a Hasse diagram.