- FindStat

Identifier

Mp00013: Binary trees —to poset⟶ Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000175: Integer partitions ⟶ ℤ

Values

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 564 entries. <<<

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

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

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

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

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

[[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

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

[[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[.,.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

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

[[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,[.,.]],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[.,.]],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

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

[[.,[.,.]],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[.,.]],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[.,.],.],[.,[.,[.,.]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[.,.],.],[.,[[.,.],.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

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

[[[.,.],.],[[.,[.,.]],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[.,.],.],[[[.,.],.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[.,[.,.]]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[.,[.,.]]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[[.,.],.]],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[[.,.],.]],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

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

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

[[[.,[.,.]],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[.,[.,.]],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[[.,.],.],.],[.,[.,.]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[[[.,.],.],.],[[.,.],.]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => [13] => 0

[[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

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

[[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[[.,.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => [15] => 0

[[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

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

[[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

[[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => [11] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

[.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[.,[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[.,.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[.,[[.,.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

[.,[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[.,.]],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

[.,[[[.,.],.],[[.,[.,.]],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[[.,.],.]],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

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

[.,[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[.,[.,.]],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[.,[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[.,[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[.,[[[.,.],.],.]],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[[.,.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[[.,.],[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[[.,[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[[[.,.],.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[.,[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[[.,[[.,.],.]],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[.,[[[[.,[.,.]],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

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

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

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

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

[.,[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[.,[[.,.],[[.,.],.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[.,[[[.,.],.],[.,.]]],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[.,[[[[.,.],[.,[.,.]]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[[[.,.],[[.,.],.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[[[.,[.,.]],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[.,[[[[[.,.],.],[.,.]],.],.]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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

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

[[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

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

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

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

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

[[.,.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

[[.,.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

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

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

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

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

[[.,.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

[[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,.]],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[[.,[[.,.],.]],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[[[.,[.,.]],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,.],.],[[[[.,.],.],.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,[.,[.,.]]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,[[.,.],.]]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[.,[[.,.],.]]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[[.,[.,.]],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[[.,[.,.]],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[[[.,.],.],.]],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[.,[[[.,.],.],.]],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,[.,[.,.]]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,[[.,.],.]],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[.,[[.,.],.]],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[[.,[.,.]],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

[[[[[.,.],.],.],.],[[.,.],.]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => [16] => 0

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

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

[[.,[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

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

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

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

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

[[.,[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

[[[.,[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

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

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

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

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

[[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => [11,2,2] => 2

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

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

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

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

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

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

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

[[.,[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[.,[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[.,[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

[[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[[[.,.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,.],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[.,.],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[.,.],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[.,.],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[.,.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[[[.,.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[.,.]],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

[[[.,[.,.]],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[.,.]],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[.,.],.],[.,[[.,.],.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

[[[[.,.],.],[[.,[.,.]],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[.,.],.],[[[.,.],.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[.,[.,.]]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[[.,.],.]],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[[.,.],.]],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

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

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

[[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[.,[.,.]],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[[[.,.],.],.],[[.,.],.]],.] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => [14] => 0

[[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,[.,[[.,.],.]]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[[[.,[[.,[.,.]],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[.,[[[.,.],.],.]],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[[.,.],[[.,.],.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => [16] => 0

[[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[[.,[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

[[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

[[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => [12] => 0

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

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

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

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

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

[[[.,[[.,.],[.,[.,.]]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[.,[[.,.],[[.,.],.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[.,[[.,[.,.]],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[.,[[[.,.],.],[.,.]]],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[[[.,.],[[.,.],.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

[[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => [10] => 0

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

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

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

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

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

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$F_{1} = 1$

$F_{2} = 2$

$F_{3} = 4 + q$

$F_{4} = 12 + 2\ q$

$F_{5} = 24 + 12\ q + 6\ q^{2}$

$F_{6} = 88 + 24\ q + 12\ q^{2} + 8\ q^{5}$

Description

Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape.
Given a partition

$\lambda$ with

$r$ parts, the number of semi-standard Young-tableaux of shape

$k\lambda$ and boxes with values in

$[r]$ grows as a polynomial in

$k$ . This follows by setting

$q=1$ in (7.105) on page 375 of [1], which yields the polynomial

$p(k) = \prod_{i < j}\frac{k(\lambda_j-\lambda_i)+j-i}{j-i}.$
The statistic of the degree of this polynomial.
For example, the partition

$(3, 2, 1, 1, 1)$ gives

$p(k) = \frac{-1}{36} (k - 3) (2k - 3) (k - 2)^2 (k - 1)^3$
which has degree 7 in

$k$ . Thus,

$[3, 2, 1, 1, 1] \mapsto 7$ .
This is the same as the number of unordered pairs of different parts, which follows from:

$\deg p(k)=\sum_{i < j}\begin{cases}1& \lambda_j \neq \lambda_i\\0&\lambda_i=\lambda_j\end{cases}=\sum_{\stackrel{i < j}{\lambda_j \neq \lambda_i}} 1$

Map

rowmotion cycle type

Description

The cycle type of rowmotion on the order ideals of a poset.

Map

to poset

Description

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