- FindStat

Identifier

Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤ

Values

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

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

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

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

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

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

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

[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => ([],4) => 24

[[],[],[[]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => ([(2,3)],4) => 12

[[],[[]],[]] => [.,[[.,.],[.,.]]] => [4,2,3,1] => ([(2,3)],4) => 12

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

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

[[[]],[],[]] => [[.,.],[.,[.,.]]] => [4,3,1,2] => ([(2,3)],4) => 12

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

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

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

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

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

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

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

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

[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => ([],5) => 120

[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => ([(3,4)],5) => 60

[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => ([(3,4)],5) => 60

[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 40

[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 20

[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => ([(3,4)],5) => 60

[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 30

[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 40

[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 20

[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 30

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

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

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

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

[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => ([(3,4)],5) => 60

[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 30

[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 30

[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 20

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

[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 40

[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 20

[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 20

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

[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 30

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

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

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

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

[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 24

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => ([],6) => 720

[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => ([(4,5)],6) => 360

[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => ([(4,5)],6) => 360

[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 240

[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 120

[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => ([(4,5)],6) => 360

[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 180

[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 240

[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 120

[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 180

[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 90

[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 90

[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 60

[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 30

[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => ([(4,5)],6) => 360

[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 180

[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 180

[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 120

[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 60

[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 240

[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 120

[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 120

[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 60

[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 180

[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 90

[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 90

[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 60

[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 30

[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 144

[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 48

[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 24

[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 36

[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 48

[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 24

[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 36

>>> Load all 362 entries. <<<

[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 18

[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 18

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

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

[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => ([(4,5)],6) => 360

[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 180

[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 180

[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 120

[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 60

[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 180

[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 90

[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 120

[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 60

[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 90

[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 45

[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 45

[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 30

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

[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 240

[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 120

[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 120

[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 60

[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 120

[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 60

[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 80

[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 40

[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 40

[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 20

[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 180

[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 90

[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 90

[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 60

[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 30

[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 90

[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 45

[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 45

[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 30

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

[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 144

[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 48

[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 24

[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 72

[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 36

[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 48

[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 24

[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 36

[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 18

[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 18

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

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

[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 120

[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 60

[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 60

[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 40

[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 20

[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 60

[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 30

[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 40

[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 20

[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 30

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

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

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

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

[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 60

[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 30

[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 30

[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 20

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

[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 40

[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 20

[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 20

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

[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 30

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

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

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

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

[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 24

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

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

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

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

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

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

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

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

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

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

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

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

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

[[[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 720

[[[],[],[],[],[[]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 360

[[[],[],[],[[]],[]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 360

[[[],[],[],[[],[]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 240

[[[],[],[],[[[]]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 120

[[[],[],[[]],[],[]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 360

[[[],[],[[]],[[]]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[],[],[[],[]],[]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 240

[[[],[],[[[]]],[]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 120

[[[],[],[[],[],[]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 180

[[[],[],[[],[[]]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[],[],[[[]],[]]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[],[],[[[],[]]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 60

[[[],[],[[[[]]]]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 30

[[[],[[]],[],[],[]]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 360

[[[],[[]],[],[[]]]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[],[[]],[[]],[]]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[],[[]],[[],[]]]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[],[[]],[[[]]]]] => [[.,[[.,.],[[[.,.],.],.]]],.] => [4,5,6,2,3,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[],[[],[]],[],[]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 240

[[[],[[[]]],[],[]]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 120

[[[],[[],[]],[[]]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[],[[[]]],[[]]]] => [[.,[[[.,.],.],[[.,.],.]]],.] => [5,6,2,3,4,1,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[],[[],[],[]],[]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 180

[[[],[[],[[]]],[]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[],[[[]],[]],[]]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[],[[[],[]]],[]]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 60

[[[],[[[[]]]],[]]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 30

[[[],[[],[],[],[]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 144

[[[],[[],[],[[]]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[],[[],[[]],[]]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[],[[],[[],[]]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 48

[[[],[[],[[[]]]]]] => [[.,[[.,[[[.,.],.],.]],.]],.] => [3,4,5,2,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 24

[[[],[[[]],[],[]]]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[],[[[]],[[]]]]] => [[.,[[[.,.],[[.,.],.]],.]],.] => [4,5,2,3,6,1,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 36

[[[],[[[],[]],[]]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 48

[[[],[[[[]]],[]]]] => [[.,[[[[.,.],.],[.,.]],.]],.] => [5,2,3,4,6,1,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 24

[[[],[[[],[],[]]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 36

[[[],[[[],[[]]]]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 18

[[[],[[[[]],[]]]]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 18

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

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

[[[[]],[],[],[],[]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 360

[[[[]],[],[],[[]]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[[]],[],[[]],[]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[[]],[],[[],[]]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[[]],[],[[[]]]]] => [[[.,.],[.,[[[.,.],.],.]]],.] => [4,5,6,3,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[[]],[[]],[],[]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 180

[[[[]],[[]],[[]]]] => [[[.,.],[[.,.],[[.,.],.]]],.] => [5,6,3,4,1,2,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => 90

[[[[]],[[],[]],[]]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[[]],[[[]]],[]]] => [[[.,.],[[[.,.],.],[.,.]]],.] => [6,3,4,5,1,2,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[[]],[[],[],[]]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 90

[[[[]],[[],[[]]]]] => [[[.,.],[[.,[[.,.],.]],.]],.] => [4,5,3,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 45

[[[[]],[[[]],[]]]] => [[[.,.],[[[.,.],[.,.]],.]],.] => [5,3,4,6,1,2,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 45

[[[[]],[[[],[]]]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 30

[[[[]],[[[[]]]]]] => [[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 15

[[[[],[]],[],[],[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 240

[[[[[]]],[],[],[]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 120

[[[[],[]],[],[[]]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[[[]]],[],[[]]]] => [[[[.,.],.],[.,[[.,.],.]]],.] => [5,6,4,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[[],[]],[[]],[]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 120

[[[[[]]],[[]],[]]] => [[[[.,.],.],[[.,.],[.,.]]],.] => [6,4,5,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => 60

[[[[],[]],[[],[]]]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 80

[[[[],[]],[[[]]]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 40

[[[[[]]],[[],[]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 40

[[[[[]]],[[[]]]]] => [[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => 20

[[[[],[],[]],[],[]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 180

[[[[],[[]]],[],[]]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[[[]],[]],[],[]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 90

[[[[[],[]]],[],[]]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 60

[[[[[[]]]],[],[]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 30

[[[[],[],[]],[[]]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 90

[[[[],[[]]],[[]]]] => [[[.,[[.,.],.]],[[.,.],.]],.] => [5,6,2,3,1,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 45

[[[[[]],[]],[[]]]] => [[[[.,.],[.,.]],[[.,.],.]],.] => [5,6,3,1,2,4,7] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => 45

[[[[[],[]]],[[]]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 30

[[[[[[]]]],[[]]]] => [[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => 15

[[[[],[],[],[]],[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 144

[[[[],[],[[]]],[]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[[],[[]],[]],[]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[[],[[],[]]],[]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 48

[[[[],[[[]]]],[]]] => [[[.,[[[.,.],.],.]],[.,.]],.] => [6,2,3,4,1,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 24

[[[[[]],[],[]],[]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 72

[[[[[]],[[]]],[]]] => [[[[.,.],[[.,.],.]],[.,.]],.] => [6,3,4,1,2,5,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 36

[[[[[],[]],[]],[]]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 48

[[[[[[]]],[]],[]]] => [[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => 24

[[[[[],[],[]]],[]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 36

[[[[[],[[]]]],[]]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 18

[[[[[[]],[]]],[]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 18

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

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

[[[[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 120

[[[[],[],[],[[]]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 60

[[[[],[],[[]],[]]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 60

[[[[],[],[[],[]]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 40

[[[[],[],[[[]]]]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 20

[[[[],[[]],[],[]]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 60

[[[[],[[]],[[]]]]] => [[[.,[[.,.],[[.,.],.]]],.],.] => [4,5,2,3,1,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 30

[[[[],[[],[]],[]]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 40

[[[[],[[[]]],[]]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 20

[[[[],[[],[],[]]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 30

[[[[],[[],[[]]]]]] => [[[.,[[.,[[.,.],.]],.]],.],.] => [3,4,2,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 15

[[[[],[[[]],[]]]]] => [[[.,[[[.,.],[.,.]],.]],.],.] => [4,2,3,5,1,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 15

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

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

[[[[[]],[],[],[]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 60

[[[[[]],[],[[]]]]] => [[[[.,.],[.,[[.,.],.]]],.],.] => [4,5,3,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 30

[[[[[]],[[]],[]]]] => [[[[.,.],[[.,.],[.,.]]],.],.] => [5,3,4,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => 30

[[[[[]],[[],[]]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 20

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

[[[[[],[]],[],[]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 40

[[[[[[]]],[],[]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 20

[[[[[],[]],[[]]]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 20

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

[[[[[],[],[]],[]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 30

[[[[[],[[]]],[]]]] => [[[[.,[[.,.],.]],[.,.]],.],.] => [5,2,3,1,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 15

[[[[[[]],[]],[]]]] => [[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => 15

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

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

[[[[[],[],[],[]]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 24

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => ([],8) => 40320

[[],[],[],[],[[]],[[]]] => [.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] => [7,8,5,6,4,3,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[],[[]],[],[[]]] => [.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] => [7,8,6,4,5,3,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[],[[]],[[]],[]] => [.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] => [8,6,7,4,5,3,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[[]],[],[],[[]]] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[[]],[],[[]],[]] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[[]],[[]],[],[]] => [.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] => [8,7,5,6,3,4,2,1] => ([(4,7),(5,6)],8) => 10080

[[],[],[[],[]],[[],[]]] => [.,[.,[[.,[.,.]],[[.,[.,.]],.]]]] => [7,6,8,4,3,5,2,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 4480

[[],[],[[[]]],[[[]]]] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[],[[]],[],[],[],[[]]] => [.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,2,3,1] => ([(4,7),(5,6)],8) => 10080

[[],[[]],[],[],[[]],[]] => [.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,2,3,1] => ([(4,7),(5,6)],8) => 10080

[[],[[]],[],[[]],[],[]] => [.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,2,3,1] => ([(4,7),(5,6)],8) => 10080

[[],[[]],[[]],[],[],[]] => [.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,2,3,1] => ([(4,7),(5,6)],8) => 10080

[[],[[],[]],[],[[],[]]] => [.,[[.,[.,.]],[.,[[.,[.,.]],.]]]] => [7,6,8,5,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 4480

[[],[[[]]],[],[[[]]]] => [.,[[[.,.],.],[.,[[[.,.],.],.]]]] => [6,7,8,5,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[],[[],[]],[[],[]],[]] => [.,[[.,[.,.]],[[.,[.,.]],[.,.]]]] => [8,6,5,7,3,2,4,1] => ([(2,7),(3,7),(4,6),(5,6)],8) => 4480

[[],[[[]]],[[[]]],[]] => [.,[[[.,.],.],[[[.,.],.],[.,.]]]] => [8,5,6,7,2,3,4,1] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[[]],[],[],[],[],[[]]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2] => ([(4,7),(5,6)],8) => 10080

[[[]],[],[],[],[[]],[]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2] => ([(4,7),(5,6)],8) => 10080

[[[]],[],[],[[]],[],[]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => [8,7,5,6,4,3,1,2] => ([(4,7),(5,6)],8) => 10080

[[[]],[],[[]],[],[],[]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2] => ([(4,7),(5,6)],8) => 10080

[[[]],[[]],[],[],[],[]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8) => 10080

[[[]],[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => [7,8,5,6,3,4,1,2] => ([(0,7),(1,6),(2,5),(3,4)],8) => 2520

[[[],[]],[],[],[[],[]]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,2,1,3] => ([(2,7),(3,7),(4,6),(5,6)],8) => 4480

[[[[]]],[],[],[[[]]]] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[[[]]],[],[[[]]],[]] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[[[]]],[[[]]],[],[]] => [[[.,.],.],[[[.,.],.],[.,[.,.]]]] => [8,7,4,5,6,1,2,3] => ([(2,5),(3,4),(4,6),(5,7)],8) => 1120

[[[],[],[]],[[],[],[]]] => [[.,[.,[.,.]]],[[.,[.,[.,.]]],.]] => [7,6,5,8,3,2,1,4] => ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) => 2520

[[[],[[]]],[[],[[]]]] => [[.,[[.,.],.]],[[.,[[.,.],.]],.]] => [6,7,5,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => 630

[[[],[[]]],[[[]],[]]] => [[.,[[.,.],.]],[[[.,.],[.,.]],.]] => [7,5,6,8,2,3,1,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => 630

[[[[]],[]],[[],[[]]]] => [[[.,.],[.,.]],[[.,[[.,.],.]],.]] => [6,7,5,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => 630

[[[[]],[]],[[[]],[]]] => [[[.,.],[.,.]],[[[.,.],[.,.]],.]] => [7,5,6,8,3,1,2,4] => ([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7)],8) => 630

[[[[],[]]],[[[],[]]]] => [[[.,[.,.]],.],[[[.,[.,.]],.],.]] => [6,5,7,8,2,1,3,4] => ([(0,6),(1,6),(2,7),(3,7),(6,5),(7,4)],8) => 280

[[[[[]]]],[[[[]]]]] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4] => ([(0,7),(1,6),(4,2),(5,3),(6,4),(7,5)],8) => 70

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

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

$F_{3} = q + q^{2}$

$F_{4} = q + q^{2} + 2\ q^{3} + q^{6}$

$F_{5} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{6} + 2\ q^{8} + 3\ q^{12} + q^{24}$

$F_{6} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 2\ q^{6} + 2\ q^{8} + 4\ q^{10} + 3\ q^{12} + 4\ q^{15} + 5\ q^{20} + q^{24} + 5\ q^{30} + 3\ q^{40} + 4\ q^{60} + q^{120}$

$F_{7} = q + q^{2} + 2\ q^{3} + 2\ q^{4} + 2\ q^{5} + 4\ q^{6} + 2\ q^{8} + 4\ q^{10} + 5\ q^{12} + 6\ q^{15} + 4\ q^{18} + 6\ q^{20} + 5\ q^{24} + 10\ q^{30} + 4\ q^{36} + 5\ q^{40} + 4\ q^{45} + 4\ q^{48} + 13\ q^{60} + 6\ q^{72} + q^{80} + 9\ q^{90} + 11\ q^{120} + 2\ q^{144} + 9\ q^{180} + 4\ q^{240} + 5\ q^{360} + q^{720}$

Description

The number of linear extensions of a poset.

Map

to 132-avoiding permutation

Description

Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

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

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

$w \leq y$ and

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

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

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

Map

to binary tree: right brother = right child

Description

Return a binary tree of size

$n-1$ (where

$n$ is the size of an ordered tree

$t$ ) obtained from

$t$ by the following recursive rule:
- if

$x$ is the right brother of

$y$ in

$t$ , then

$x$ becomes the right child of

$y$ ;
- if

$x$ is the first child of

$y$ in

$t$ , then

$x$ becomes the left child of

$y$ ,
and removing the root of

$t$ .