Identifier
Values
[[],[]] => [.,[.,.]] => [2,1] => ([],2) => 2
[[[]]] => [[.,.],.] => [1,2] => ([(0,1)],2) => 3
[[],[],[]] => [.,[.,[.,.]]] => [3,2,1] => ([],3) => 3
[[],[[]]] => [.,[[.,.],.]] => [2,3,1] => ([(1,2)],3) => 4
[[[]],[]] => [[.,.],[.,.]] => [3,1,2] => ([(1,2)],3) => 4
[[[],[]]] => [[.,[.,.]],.] => [2,1,3] => ([(0,2),(1,2)],3) => 5
[[[[]]]] => [[[.,.],.],.] => [1,2,3] => ([(0,2),(2,1)],3) => 6
[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => ([],4) => 4
[[],[],[[]]] => [.,[.,[[.,.],.]]] => [3,4,2,1] => ([(2,3)],4) => 5
[[],[[]],[]] => [.,[[.,.],[.,.]]] => [4,2,3,1] => ([(2,3)],4) => 5
[[],[[],[]]] => [.,[[.,[.,.]],.]] => [3,2,4,1] => ([(1,3),(2,3)],4) => 6
[[],[[[]]]] => [.,[[[.,.],.],.]] => [2,3,4,1] => ([(1,2),(2,3)],4) => 7
[[[]],[],[]] => [[.,.],[.,[.,.]]] => [4,3,1,2] => ([(2,3)],4) => 5
[[[]],[[]]] => [[.,.],[[.,.],.]] => [3,4,1,2] => ([(0,3),(1,2)],4) => 6
[[[],[]],[]] => [[.,[.,.]],[.,.]] => [4,2,1,3] => ([(1,3),(2,3)],4) => 6
[[[[]]],[]] => [[[.,.],.],[.,.]] => [4,1,2,3] => ([(1,2),(2,3)],4) => 7
[[[],[],[]]] => [[.,[.,[.,.]]],.] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4) => 7
[[[],[[]]]] => [[.,[[.,.],.]],.] => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4) => 8
[[[[]],[]]] => [[[.,.],[.,.]],.] => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4) => 8
[[[[],[]]]] => [[[.,[.,.]],.],.] => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4) => 9
[[[[[]]]]] => [[[[.,.],.],.],.] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 10
[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => ([],5) => 5
[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => ([(3,4)],5) => 6
[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => ([(3,4)],5) => 6
[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => ([(2,4),(3,4)],5) => 7
[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => ([(2,3),(3,4)],5) => 8
[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => ([(3,4)],5) => 6
[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => ([(1,4),(2,3)],5) => 7
[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => ([(2,4),(3,4)],5) => 7
[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => 8
[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5) => 8
[[],[[],[[]]]] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5) => 9
[[],[[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5) => 9
[[],[[[],[]]]] => [.,[[[.,[.,.]],.],.]] => [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) => 11
[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => ([(3,4)],5) => 6
[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => ([(1,4),(2,3)],5) => 7
[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => 7
[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5) => 8
[[[]],[[[]]]] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5) => 9
[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => ([(2,4),(3,4)],5) => 7
[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => 8
[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5) => 8
[[[[]]],[[]]] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => 9
[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5) => 8
[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5) => 9
[[[[]],[]],[]] => [[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5) => 9
[[[[],[]]],[]] => [[[.,[.,.]],.],[.,.]] => [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) => 11
[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5) => 9
[[[],[],[[]]]] => [[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10
[[[],[[]],[]]] => [[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10
[[[],[[],[]]]] => [[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 11
[[[],[[[]]]]] => [[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 12
[[[[]],[],[]]] => [[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => ([(0,4),(1,4),(2,3),(3,4)],5) => 10
[[[[]],[[]]]] => [[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => 11
[[[[],[]],[]]] => [[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5) => 11
[[[[[]]],[]]] => [[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => 12
[[[[],[],[]]]] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5) => 12
[[[[],[[]]]]] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 13
[[[[[]],[]]]] => [[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => ([(0,4),(1,2),(2,4),(4,3)],5) => 13
[[[[[],[]]]]] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5) => 14
[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 15
[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => ([],6) => 6
[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => ([(4,5)],6) => 7
[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => ([(4,5)],6) => 7
[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => ([(3,5),(4,5)],6) => 8
[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => ([(3,4),(4,5)],6) => 9
[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => ([(4,5)],6) => 7
[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => 8
[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => ([(3,5),(4,5)],6) => 8
[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => ([(3,4),(4,5)],6) => 9
[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => ([(2,5),(3,5),(4,5)],6) => 9
[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 10
[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => ([(2,5),(3,4),(4,5)],6) => 10
[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => ([(2,5),(3,5),(5,4)],6) => 11
[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => ([(2,3),(3,5),(5,4)],6) => 12
[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => ([(4,5)],6) => 7
[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => ([(2,5),(3,4)],6) => 8
[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => ([(2,5),(3,4)],6) => 8
[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => ([(1,5),(2,5),(3,4)],6) => 9
[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => ([(1,3),(2,4),(4,5)],6) => 10
[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => ([(3,5),(4,5)],6) => 8
[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => ([(3,4),(4,5)],6) => 9
[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => ([(1,5),(2,5),(3,4)],6) => 9
[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => ([(1,3),(2,4),(4,5)],6) => 10
[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => ([(2,5),(3,5),(4,5)],6) => 9
[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => ([(2,5),(3,4),(4,5)],6) => 10
[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => ([(2,5),(3,4),(4,5)],6) => 10
[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => ([(2,5),(3,5),(5,4)],6) => 11
[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => 12
[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10
[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12
[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13
[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => ([(1,4),(2,3),(3,5),(4,5)],6) => 12
[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12
[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13
[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => ([(1,5),(2,5),(3,5),(5,4)],6) => 13
>>> Load all 473 entries. <<<
[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14
[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14
[[],[[[[],[]]]]] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => ([(1,5),(2,5),(3,4),(5,3)],6) => 15
[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => ([(1,5),(3,4),(4,2),(5,3)],6) => 16
[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => ([(4,5)],6) => 7
[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => ([(2,5),(3,4)],6) => 8
[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => ([(2,5),(3,4)],6) => 8
[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => ([(1,5),(2,5),(3,4)],6) => 9
[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => ([(1,3),(2,4),(4,5)],6) => 10
[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => 8
[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => ([(0,5),(1,4),(2,3)],6) => 9
[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => ([(1,5),(2,5),(3,4)],6) => 9
[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => ([(1,3),(2,4),(4,5)],6) => 10
[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10
[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11
[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11
[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => ([(0,5),(1,5),(2,3),(5,4)],6) => 12
[[[]],[[[[]]]]] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => ([(0,5),(1,3),(4,2),(5,4)],6) => 13
[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => ([(3,5),(4,5)],6) => 8
[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => 9
[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9
[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 10
[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => ([(1,5),(2,5),(3,4)],6) => 9
[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => 10
[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => ([(0,5),(1,5),(2,4),(3,4)],6) => 10
[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 11
[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => 11
[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => ([(0,5),(1,4),(4,2),(5,3)],6) => 12
[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => ([(2,5),(3,5),(4,5)],6) => 9
[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => ([(2,5),(3,4),(4,5)],6) => 10
[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => ([(2,5),(3,4),(4,5)],6) => 10
[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => ([(2,5),(3,5),(5,4)],6) => 11
[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => 12
[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => ([(0,5),(1,5),(2,5),(3,4)],6) => 10
[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11
[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => ([(0,5),(1,3),(2,4),(4,5)],6) => 11
[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => ([(0,5),(1,5),(2,3),(5,4)],6) => 12
[[[[[]]]],[[]]] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => ([(0,5),(1,3),(4,2),(5,4)],6) => 13
[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => ([(1,5),(2,5),(3,5),(4,5)],6) => 10
[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12
[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13
[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => ([(1,5),(2,5),(3,4),(4,5)],6) => 11
[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => 12
[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => ([(1,5),(2,4),(3,4),(4,5)],6) => 12
[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => 13
[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => ([(1,5),(2,5),(3,5),(5,4)],6) => 13
[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14
[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => ([(1,5),(2,3),(3,5),(5,4)],6) => 14
[[[[[],[]]]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => ([(1,5),(2,5),(3,4),(5,3)],6) => 15
[[[[[[]]]]],[]] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => 16
[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 11
[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12
[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12
[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13
[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14
[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12
[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13
[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13
[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14
[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 14
[[[],[[],[[]]]]] => [[.,[[.,[[.,.],.]],.]],.] => [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) => 16
[[[],[[[[]]]]]] => [[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 17
[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => 12
[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13
[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => 13
[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 14
[[[[]],[[[]]]]] => [[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 15
[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => 13
[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 14
[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => 14
[[[[[]]],[[]]]] => [[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => 15
[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => 14
[[[[],[[]]],[]]] => [[[.,[[.,.],.]],[.,.]],.] => [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) => 16
[[[[[[]]]],[]]] => [[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => 17
[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => 15
[[[[],[],[[]]]]] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16
[[[[],[[]],[]]]] => [[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16
[[[[],[[],[]]]]] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 17
[[[[],[[[]]]]]] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 18
[[[[[]],[],[]]]] => [[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => 16
[[[[[]],[[]]]]] => [[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => 17
[[[[[],[]],[]]]] => [[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => 17
[[[[[[]]],[]]]] => [[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => 18
[[[[[],[],[]]]]] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => 18
[[[[[],[[]]]]]] => [[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 19
[[[[[[]],[]]]]] => [[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => 19
[[[[[[],[]]]]]] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 20
[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 21
[[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => ([],7) => 7
[[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => ([(5,6)],7) => 8
[[],[],[],[],[[]],[]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1] => ([(5,6)],7) => 8
[[],[],[],[],[[],[]]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => ([(4,6),(5,6)],7) => 9
[[],[],[],[],[[[]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1] => ([(4,5),(5,6)],7) => 10
[[],[],[],[[]],[],[]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => [7,6,4,5,3,2,1] => ([(5,6)],7) => 8
[[],[],[],[[]],[[]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => [6,7,4,5,3,2,1] => ([(3,6),(4,5)],7) => 9
[[],[],[],[[],[]],[]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => [7,5,4,6,3,2,1] => ([(4,6),(5,6)],7) => 9
[[],[],[],[[[]]],[]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => [7,4,5,6,3,2,1] => ([(4,5),(5,6)],7) => 10
[[],[],[],[[],[],[]]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => ([(3,6),(4,6),(5,6)],7) => 10
[[],[],[],[[[],[]]]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1] => ([(3,6),(4,6),(6,5)],7) => 12
[[],[],[],[[[[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => ([(3,4),(4,6),(6,5)],7) => 13
[[],[],[[]],[],[],[]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1] => ([(5,6)],7) => 8
[[],[],[[]],[],[[]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1] => ([(3,6),(4,5)],7) => 9
[[],[],[[]],[[]],[]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => [7,5,6,3,4,2,1] => ([(3,6),(4,5)],7) => 9
[[],[],[[]],[[],[]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[],[[],[]],[],[]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => [7,6,4,3,5,2,1] => ([(4,6),(5,6)],7) => 9
[[],[],[[[]]],[],[]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1] => ([(4,5),(5,6)],7) => 10
[[],[],[[],[]],[[]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => [6,7,4,3,5,2,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[],[[],[],[]],[]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => [7,5,4,3,6,2,1] => ([(3,6),(4,6),(5,6)],7) => 10
[[],[],[[[],[]]],[]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => [7,4,3,5,6,2,1] => ([(3,6),(4,6),(6,5)],7) => 12
[[],[],[[[[]]]],[]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1] => ([(3,4),(4,6),(6,5)],7) => 13
[[],[],[[],[],[],[]]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[[],[],[[],[],[[]]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => [5,6,4,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[],[[],[[]],[]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => [6,4,5,3,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[],[[],[[],[]]]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => [5,4,6,3,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[],[],[[[]],[],[]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [6,5,3,4,7,2,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[],[[[],[]],[]]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [6,4,3,5,7,2,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[],[],[[[],[],[]]]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14
[[],[],[[[[],[]]]]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16
[[],[[]],[],[],[],[]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => [7,6,5,4,2,3,1] => ([(5,6)],7) => 8
[[],[[]],[],[],[[]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => [6,7,5,4,2,3,1] => ([(3,6),(4,5)],7) => 9
[[],[[]],[],[[]],[]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => [7,5,6,4,2,3,1] => ([(3,6),(4,5)],7) => 9
[[],[[]],[],[[],[]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => [6,5,7,4,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[[]],[[]],[],[]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => [7,6,4,5,2,3,1] => ([(3,6),(4,5)],7) => 9
[[],[[]],[[],[]],[]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => [7,5,4,6,2,3,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[[]],[[],[],[]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => [6,5,4,7,2,3,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[],[[]],[[[],[]]]] => [.,[[.,.],[[[.,[.,.]],.],.]]] => [5,4,6,7,2,3,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[],[[],[]],[],[],[]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => [7,6,5,3,2,4,1] => ([(4,6),(5,6)],7) => 9
[[],[[[]]],[],[],[]] => [.,[[[.,.],.],[.,[.,[.,.]]]]] => [7,6,5,2,3,4,1] => ([(4,5),(5,6)],7) => 10
[[],[[],[]],[],[[]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => [6,7,5,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[[],[]],[[]],[]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => [7,5,6,3,2,4,1] => ([(2,6),(3,6),(4,5)],7) => 10
[[],[[],[]],[[],[]]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => [6,5,7,3,2,4,1] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[[],[[],[]],[[[]]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => [5,6,7,3,2,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[],[[[]]],[[],[]]] => [.,[[[.,.],.],[[.,[.,.]],.]]] => [6,5,7,2,3,4,1] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[],[[],[],[]],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => [7,6,4,3,2,5,1] => ([(3,6),(4,6),(5,6)],7) => 10
[[],[[[],[]]],[],[]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => [7,6,3,2,4,5,1] => ([(3,6),(4,6),(6,5)],7) => 12
[[],[[[[]]]],[],[]] => [.,[[[[.,.],.],.],[.,[.,.]]]] => [7,6,2,3,4,5,1] => ([(3,4),(4,6),(6,5)],7) => 13
[[],[[],[],[]],[[]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => [6,7,4,3,2,5,1] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[],[[[],[]]],[[]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => [6,7,3,2,4,5,1] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[],[[],[],[],[]],[]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[[],[[],[],[[]]],[]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => [7,4,5,3,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[[],[[]],[]],[]] => [.,[[.,[[.,.],[.,.]]],[.,.]]] => [7,5,3,4,2,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[[],[[],[]]],[]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => [7,4,3,5,2,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[],[[[]],[],[]],[]] => [.,[[[.,.],[.,[.,.]]],[.,.]]] => [7,5,4,2,3,6,1] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[],[[[],[]],[]],[]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => [7,5,3,2,4,6,1] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[],[[[],[],[]]],[]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14
[[],[[[[],[]]]],[]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16
[[],[[],[],[],[],[]]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12
[[],[[],[],[],[[]]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[],[[],[],[[]],[]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => [6,4,5,3,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[],[[],[],[[],[]]]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[],[[],[],[[[]]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[],[[],[[]],[],[]]] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[],[[],[[],[]],[]]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => [6,4,3,5,2,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[],[[],[[[]]],[]]] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[],[[],[[],[],[]]]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15
[[],[[],[[[],[]]]]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => [4,3,5,6,2,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17
[[],[[],[[[[]]]]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18
[[],[[[]],[],[],[]]] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [6,5,4,2,3,7,1] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[],[[[]],[[],[]]]] => [.,[[[.,.],[[.,[.,.]],.]],.]] => [5,4,6,2,3,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[],[[[],[]],[],[]]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[],[[[[]]],[],[]]] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [6,5,2,3,4,7,1] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[],[[[],[]],[[]]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => [5,6,3,2,4,7,1] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[],[[[],[],[]],[]]] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15
[[],[[[[],[]]],[]]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [6,3,2,4,5,7,1] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17
[[],[[[[[]]]],[]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [6,2,3,4,5,7,1] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18
[[],[[[],[],[],[]]]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 16
[[],[[[],[],[[]]]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[],[[[],[[]],[]]]] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[],[[[],[[],[]]]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18
[[],[[[[]],[],[]]]] => [.,[[[[.,.],[.,[.,.]]],.],.]] => [5,4,2,3,6,7,1] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[],[[[[],[]],[]]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [5,3,2,4,6,7,1] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18
[[],[[[[],[],[]]]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 19
[[],[[[[[],[]]]]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 21
[[[]],[],[],[],[],[]] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => ([(5,6)],7) => 8
[[[]],[],[],[],[[]]] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2] => ([(3,6),(4,5)],7) => 9
[[[]],[],[],[[]],[]] => [[.,.],[.,[.,[[.,.],[.,.]]]]] => [7,5,6,4,3,1,2] => ([(3,6),(4,5)],7) => 9
[[[]],[],[],[[],[]]] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[[[]],[],[[]],[],[]] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2] => ([(3,6),(4,5)],7) => 9
[[[]],[],[[],[]],[]] => [[.,.],[.,[[.,[.,.]],[.,.]]]] => [7,5,4,6,3,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[[[]],[],[[],[],[]]] => [[.,.],[.,[[.,[.,[.,.]]],.]]] => [6,5,4,7,3,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[[]],[],[[[],[]]]] => [[.,.],[.,[[[.,[.,.]],.],.]]] => [5,4,6,7,3,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[[]],[[]],[],[],[]] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => 9
[[[]],[[]],[[],[]]] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[[[]],[[],[]],[],[]] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [7,6,4,3,5,1,2] => ([(2,6),(3,6),(4,5)],7) => 10
[[[]],[[],[]],[[]]] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [6,7,4,3,5,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[[[]],[[],[],[]],[]] => [[.,.],[[.,[.,[.,.]]],[.,.]]] => [7,5,4,3,6,1,2] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[[]],[[[],[]]],[]] => [[.,.],[[[.,[.,.]],.],[.,.]]] => [7,4,3,5,6,1,2] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[[]],[[],[],[],[]]] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12
[[[]],[[],[],[[]]]] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[]],[[],[[]],[]]] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[]],[[],[[],[]]]] => [[.,.],[[.,[[.,[.,.]],.]],.]] => [5,4,6,3,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14
[[[]],[[[]],[],[]]] => [[.,.],[[[.,.],[.,[.,.]]],.]] => [6,5,3,4,7,1,2] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[]],[[[],[]],[]]] => [[.,.],[[[.,[.,.]],[.,.]],.]] => [6,4,3,5,7,1,2] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14
[[[]],[[[],[],[]]]] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 15
[[[]],[[[[],[]]]]] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 17
[[[],[]],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,.]]]]] => [7,6,5,4,2,1,3] => ([(4,6),(5,6)],7) => 9
[[[[]]],[],[],[],[]] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => 10
[[[],[]],[],[],[[]]] => [[.,[.,.]],[.,[.,[[.,.],.]]]] => [6,7,5,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[[[],[]],[],[[]],[]] => [[.,[.,.]],[.,[[.,.],[.,.]]]] => [7,5,6,4,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[[[],[]],[],[[],[]]] => [[.,[.,.]],[.,[[.,[.,.]],.]]] => [6,5,7,4,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[[[],[]],[],[[[]]]] => [[.,[.,.]],[.,[[[.,.],.],.]]] => [5,6,7,4,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[[[]]],[],[[],[]]] => [[[.,.],.],[.,[[.,[.,.]],.]]] => [6,5,7,4,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[[],[]],[[]],[],[]] => [[.,[.,.]],[[.,.],[.,[.,.]]]] => [7,6,4,5,2,1,3] => ([(2,6),(3,6),(4,5)],7) => 10
[[[],[]],[[]],[[]]] => [[.,[.,.]],[[.,.],[[.,.],.]]] => [6,7,4,5,2,1,3] => ([(0,6),(1,6),(2,5),(3,4)],7) => 11
[[[],[]],[[],[]],[]] => [[.,[.,.]],[[.,[.,.]],[.,.]]] => [7,5,4,6,2,1,3] => ([(1,6),(2,6),(3,5),(4,5)],7) => 11
[[[],[]],[[[]]],[]] => [[.,[.,.]],[[[.,.],.],[.,.]]] => [7,4,5,6,2,1,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[[[]]],[[],[]],[]] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [7,5,4,6,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => 12
[[[],[]],[[],[],[]]] => [[.,[.,.]],[[.,[.,[.,.]]],.]] => [6,5,4,7,2,1,3] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12
[[[],[]],[[],[[]]]] => [[.,[.,.]],[[.,[[.,.],.]],.]] => [5,6,4,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13
[[[],[]],[[[]],[]]] => [[.,[.,.]],[[[.,.],[.,.]],.]] => [6,4,5,7,2,1,3] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13
[[[],[]],[[[],[]]]] => [[.,[.,.]],[[[.,[.,.]],.],.]] => [5,4,6,7,2,1,3] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 14
[[[],[]],[[[[]]]]] => [[.,[.,.]],[[[[.,.],.],.],.]] => [4,5,6,7,2,1,3] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 15
[[[[]]],[[],[],[]]] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 13
[[[[]]],[[[],[]]]] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 15
[[[],[],[]],[],[],[]] => [[.,[.,[.,.]]],[.,[.,[.,.]]]] => [7,6,5,3,2,1,4] => ([(3,6),(4,6),(5,6)],7) => 10
[[[[],[]]],[],[],[]] => [[[.,[.,.]],.],[.,[.,[.,.]]]] => [7,6,5,2,1,3,4] => ([(3,6),(4,6),(6,5)],7) => 12
[[[[[]]]],[],[],[]] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => 13
[[[],[],[]],[],[[]]] => [[.,[.,[.,.]]],[.,[[.,.],.]]] => [6,7,5,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[[[],[]]],[],[[]]] => [[[.,[.,.]],.],[.,[[.,.],.]]] => [6,7,5,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[[],[],[]],[[]],[]] => [[.,[.,[.,.]]],[[.,.],[.,.]]] => [7,5,6,3,2,1,4] => ([(1,6),(2,6),(3,6),(4,5)],7) => 11
[[[[],[]]],[[]],[]] => [[[.,[.,.]],.],[[.,.],[.,.]]] => [7,5,6,2,1,3,4] => ([(1,6),(2,6),(3,4),(6,5)],7) => 13
[[[],[],[]],[[],[]]] => [[.,[.,[.,.]]],[[.,[.,.]],.]] => [6,5,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,5),(4,5)],7) => 12
[[[],[],[]],[[[]]]] => [[.,[.,[.,.]]],[[[.,.],.],.]] => [5,6,7,3,2,1,4] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => 13
[[[],[[]]],[[],[]]] => [[.,[[.,.],.]],[[.,[.,.]],.]] => [6,5,7,2,3,1,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13
[[[[]],[]],[[],[]]] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [6,5,7,3,1,2,4] => ([(0,6),(1,5),(2,5),(3,4),(4,6)],7) => 13
[[[[],[]]],[[],[]]] => [[[.,[.,.]],.],[[.,[.,.]],.]] => [6,5,7,2,1,3,4] => ([(0,6),(1,6),(2,5),(3,5),(6,4)],7) => 14
[[[[],[]]],[[[]]]] => [[[.,[.,.]],.],[[[.,.],.],.]] => [5,6,7,2,1,3,4] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => 15
[[[[[]]]],[[],[]]] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => 15
[[[],[],[],[]],[],[]] => [[.,[.,[.,[.,.]]]],[.,[.,.]]] => [7,6,4,3,2,1,5] => ([(2,6),(3,6),(4,6),(5,6)],7) => 11
[[[],[],[[]]],[],[]] => [[.,[.,[[.,.],.]]],[.,[.,.]]] => [7,6,3,4,2,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[[],[[]],[]],[],[]] => [[.,[[.,.],[.,.]]],[.,[.,.]]] => [7,6,4,2,3,1,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[[],[[],[]]],[],[]] => [[.,[[.,[.,.]],.]],[.,[.,.]]] => [7,6,3,2,4,1,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[[[]],[],[]],[],[]] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [7,6,4,3,1,2,5] => ([(2,6),(3,6),(4,5),(5,6)],7) => 12
[[[[],[]],[]],[],[]] => [[[.,[.,.]],[.,.]],[.,[.,.]]] => [7,6,4,2,1,3,5] => ([(2,6),(3,5),(4,5),(5,6)],7) => 13
[[[[],[],[]]],[],[]] => [[[.,[.,[.,.]]],.],[.,[.,.]]] => [7,6,3,2,1,4,5] => ([(2,6),(3,6),(4,6),(6,5)],7) => 14
[[[[[],[]]]],[],[]] => [[[[.,[.,.]],.],.],[.,[.,.]]] => [7,6,2,1,3,4,5] => ([(2,6),(3,6),(4,5),(6,4)],7) => 16
[[[],[],[],[]],[[]]] => [[.,[.,[.,[.,.]]]],[[.,.],.]] => [6,7,4,3,2,1,5] => ([(0,6),(1,6),(2,6),(3,6),(4,5)],7) => 12
[[[],[],[[]]],[[]]] => [[.,[.,[[.,.],.]]],[[.,.],.]] => [6,7,3,4,2,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[],[[]],[]],[[]]] => [[.,[[.,.],[.,.]]],[[.,.],.]] => [6,7,4,2,3,1,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[],[[],[]]],[[]]] => [[.,[[.,[.,.]],.]],[[.,.],.]] => [6,7,3,2,4,1,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14
[[[[]],[],[]],[[]]] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [6,7,4,3,1,2,5] => ([(0,6),(1,6),(2,4),(3,5),(5,6)],7) => 13
[[[[],[]],[]],[[]]] => [[[.,[.,.]],[.,.]],[[.,.],.]] => [6,7,4,2,1,3,5] => ([(0,6),(1,5),(2,5),(3,4),(5,6)],7) => 14
[[[[],[],[]]],[[]]] => [[[.,[.,[.,.]]],.],[[.,.],.]] => [6,7,3,2,1,4,5] => ([(0,6),(1,6),(2,6),(3,4),(6,5)],7) => 15
[[[[[],[]]]],[[]]] => [[[[.,[.,.]],.],.],[[.,.],.]] => [6,7,2,1,3,4,5] => ([(0,6),(1,6),(2,3),(4,5),(6,4)],7) => 17
[[[],[],[],[],[]],[]] => [[.,[.,[.,[.,[.,.]]]]],[.,.]] => [7,5,4,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 12
[[[],[],[],[[]]],[]] => [[.,[.,[.,[[.,.],.]]]],[.,.]] => [7,4,5,3,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[[],[],[[]],[]],[]] => [[.,[.,[[.,.],[.,.]]]],[.,.]] => [7,5,3,4,2,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[[],[],[[],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],[.,.]] => [7,4,3,5,2,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[[],[],[[[]]]],[]] => [[.,[.,[[[.,.],.],.]]],[.,.]] => [7,3,4,5,2,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[[],[[]],[],[]],[]] => [[.,[[.,.],[.,[.,.]]]],[.,.]] => [7,5,4,2,3,1,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[[],[[],[]],[]],[]] => [[.,[[.,[.,.]],[.,.]]],[.,.]] => [7,5,3,2,4,1,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[[],[[[]]],[]],[]] => [[.,[[[.,.],.],[.,.]]],[.,.]] => [7,5,2,3,4,1,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[[],[[],[],[]]],[]] => [[.,[[.,[.,[.,.]]],.]],[.,.]] => [7,4,3,2,5,1,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15
[[[],[[[],[]]]],[]] => [[.,[[[.,[.,.]],.],.]],[.,.]] => [7,3,2,4,5,1,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17
[[[],[[[[]]]]],[]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18
[[[[]],[],[],[]],[]] => [[[.,.],[.,[.,[.,.]]]],[.,.]] => [7,5,4,3,1,2,6] => ([(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 13
[[[[]],[[],[]]],[]] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [7,4,3,5,1,2,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[[],[]],[],[]],[]] => [[[.,[.,.]],[.,[.,.]]],[.,.]] => [7,5,4,2,1,3,6] => ([(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 14
[[[[[]]],[],[]],[]] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 15
[[[[],[]],[[]]],[]] => [[[.,[.,.]],[[.,.],.]],[.,.]] => [7,4,5,2,1,3,6] => ([(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[[],[],[]],[]],[]] => [[[.,[.,[.,.]]],[.,.]],[.,.]] => [7,5,3,2,1,4,6] => ([(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 15
[[[[[],[]]],[]],[]] => [[[[.,[.,.]],.],[.,.]],[.,.]] => [7,5,2,1,3,4,6] => ([(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 17
[[[[[[]]]],[]],[]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => 18
[[[[],[],[],[]]],[]] => [[[.,[.,[.,[.,.]]]],.],[.,.]] => [7,4,3,2,1,5,6] => ([(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 16
[[[[],[],[[]]]],[]] => [[[.,[.,[[.,.],.]]],.],[.,.]] => [7,3,4,2,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[[[],[[]],[]]],[]] => [[[.,[[.,.],[.,.]]],.],[.,.]] => [7,4,2,3,1,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[[[],[[],[]]]],[]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [7,3,2,4,1,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18
[[[[[]],[],[]]],[]] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [7,4,3,1,2,5,6] => ([(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 17
[[[[[],[]],[]]],[]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [7,4,2,1,3,5,6] => ([(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 18
[[[[[],[],[]]]],[]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [7,3,2,1,4,5,6] => ([(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 19
[[[[[[],[]]]]],[]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [7,2,1,3,4,5,6] => ([(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 21
[[[],[],[],[],[],[]]] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 13
[[[],[],[],[],[[]]]] => [[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14
[[[],[],[],[[]],[]]] => [[.,[.,[.,[[.,.],[.,.]]]]],.] => [6,4,5,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14
[[[],[],[],[[],[]]]] => [[.,[.,[.,[[.,[.,.]],.]]]],.] => [5,4,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15
[[[],[],[],[[[]]]]] => [[.,[.,[.,[[[.,.],.],.]]]],.] => [4,5,6,3,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16
[[[],[],[[]],[],[]]] => [[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14
[[[],[],[[]],[[]]]] => [[.,[.,[[.,.],[[.,.],.]]]],.] => [5,6,3,4,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[],[],[[],[]],[]]] => [[.,[.,[[.,[.,.]],[.,.]]]],.] => [6,4,3,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15
[[[],[],[[[]]],[]]] => [[.,[.,[[[.,.],.],[.,.]]]],.] => [6,3,4,5,2,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16
[[[],[],[[],[],[]]]] => [[.,[.,[[.,[.,[.,.]]],.]]],.] => [5,4,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16
[[[],[],[[],[[]]]]] => [[.,[.,[[.,[[.,.],.]],.]]],.] => [4,5,3,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[],[],[[[]],[]]]] => [[.,[.,[[[.,.],[.,.]],.]]],.] => [5,3,4,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[],[],[[[],[]]]]] => [[.,[.,[[[.,[.,.]],.],.]]],.] => [4,3,5,6,2,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18
[[[],[],[[[[]]]]]] => [[.,[.,[[[[.,.],.],.],.]]],.] => [3,4,5,6,2,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19
[[[],[[]],[],[],[]]] => [[.,[[.,.],[.,[.,[.,.]]]]],.] => [6,5,4,2,3,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14
[[[],[[]],[],[[]]]] => [[.,[[.,.],[.,[[.,.],.]]]],.] => [5,6,4,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[],[[]],[[]],[]]] => [[.,[[.,.],[[.,.],[.,.]]]],.] => [6,4,5,2,3,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[],[[]],[[],[]]]] => [[.,[[.,.],[[.,[.,.]],.]]],.] => [5,4,6,2,3,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[],[[],[]],[],[]]] => [[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15
[[[],[[[]]],[],[]]] => [[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16
[[[],[[],[]],[[]]]] => [[.,[[.,[.,.]],[[.,.],.]]],.] => [5,6,3,2,4,1,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[],[[],[],[]],[]]] => [[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16
[[[],[[],[[]]],[]]] => [[.,[[.,[[.,.],.]],[.,.]]],.] => [6,3,4,2,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[],[[[]],[]],[]]] => [[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[],[[[],[]]],[]]] => [[.,[[[.,[.,.]],.],[.,.]]],.] => [6,3,2,4,5,1,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18
[[[],[[[[]]]],[]]] => [[.,[[[[.,.],.],.],[.,.]]],.] => [6,2,3,4,5,1,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19
[[[],[[],[],[],[]]]] => [[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17
[[[],[[],[],[[]]]]] => [[.,[[.,[.,[[.,.],.]]],.]],.] => [4,5,3,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[],[[],[[]],[]]]] => [[.,[[.,[[.,.],[.,.]]],.]],.] => [5,3,4,2,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[],[[],[[],[]]]]] => [[.,[[.,[[.,[.,.]],.]],.]],.] => [4,3,5,2,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19
[[[],[[[]],[],[]]]] => [[.,[[[.,.],[.,[.,.]]],.]],.] => [5,4,2,3,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[],[[[],[]],[]]]] => [[.,[[[.,[.,.]],[.,.]],.]],.] => [5,3,2,4,6,1,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19
[[[],[[[],[],[]]]]] => [[.,[[[.,[.,[.,.]]],.],.]],.] => [4,3,2,5,6,1,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 20
[[[],[[[],[[]]]]]] => [[.,[[[.,[[.,.],.]],.],.]],.] => [3,4,2,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21
[[[],[[[[]],[]]]]] => [[.,[[[[.,.],[.,.]],.],.]],.] => [4,2,3,5,6,1,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21
[[[],[[[[],[]]]]]] => [[.,[[[[.,[.,.]],.],.],.]],.] => [3,2,4,5,6,1,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 22
[[[[]],[],[],[],[]]] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => 14
[[[[]],[],[],[[]]]] => [[[.,.],[.,[.,[[.,.],.]]]],.] => [5,6,4,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[[]],[],[[]],[]]] => [[[.,.],[.,[[.,.],[.,.]]]],.] => [6,4,5,3,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[[]],[],[[],[]]]] => [[[.,.],[.,[[.,[.,.]],.]]],.] => [5,4,6,3,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[[]],[[]],[],[]]] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => 15
[[[[]],[[],[]],[]]] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [6,4,3,5,1,2,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[[]],[[],[],[]]]] => [[[.,.],[[.,[.,[.,.]]],.]],.] => [5,4,3,6,1,2,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 17
[[[[]],[[[],[]]]]] => [[[.,.],[[[.,[.,.]],.],.]],.] => [4,3,5,6,1,2,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 19
[[[[],[]],[],[],[]]] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => 15
[[[[[]]],[],[],[]]] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => 16
[[[[],[]],[],[[]]]] => [[[.,[.,.]],[.,[[.,.],.]]],.] => [5,6,4,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[[],[]],[[]],[]]] => [[[.,[.,.]],[[.,.],[.,.]]],.] => [6,4,5,2,1,3,7] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => 16
[[[[],[]],[[],[]]]] => [[[.,[.,.]],[[.,[.,.]],.]],.] => [5,4,6,2,1,3,7] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => 17
[[[[],[]],[[[]]]]] => [[[.,[.,.]],[[[.,.],.],.]],.] => [4,5,6,2,1,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 18
[[[[[]]],[[],[]]]] => [[[[.,.],.],[[.,[.,.]],.]],.] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => 18
[[[[],[],[]],[],[]]] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => 16
[[[[],[[]]],[],[]]] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [6,5,2,3,1,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[[[]],[]],[],[]]] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => 17
[[[[[],[]]],[],[]]] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [6,5,2,1,3,4,7] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => 18
[[[[[[]]]],[],[]]] => [[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => 19
[[[[],[],[]],[[]]]] => [[[.,[.,[.,.]]],[[.,.],.]],.] => [5,6,3,2,1,4,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => 17
[[[[[],[]]],[[]]]] => [[[[.,[.,.]],.],[[.,.],.]],.] => [5,6,2,1,3,4,7] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => 19
[[[[],[],[],[]],[]]] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => 17
[[[[],[],[[]]],[]]] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [6,3,4,2,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[[],[[]],[]],[]]] => [[[.,[[.,.],[.,.]]],[.,.]],.] => [6,4,2,3,1,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[[],[[],[]]],[]]] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [6,3,2,4,1,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19
[[[[[]],[],[]],[]]] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [6,4,3,1,2,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => 18
[[[[[],[]],[]],[]]] => [[[[.,[.,.]],[.,.]],[.,.]],.] => [6,4,2,1,3,5,7] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => 19
[[[[[],[],[]]],[]]] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [6,3,2,1,4,5,7] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => 20
[[[[[],[[]]]],[]]] => [[[[.,[[.,.],.]],.],[.,.]],.] => [6,2,3,1,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21
[[[[[[]],[]]],[]]] => [[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => 21
[[[[[[],[]]]],[]]] => [[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => 22
[[[[],[],[],[],[]]]] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => 18
[[[[],[],[],[[]]]]] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19
[[[[],[],[[]],[]]]] => [[[.,[.,[[.,.],[.,.]]]],.],.] => [5,3,4,2,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19
[[[[],[],[[],[]]]]] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20
[[[[],[],[[[]]]]]] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21
[[[[],[[]],[],[]]]] => [[[.,[[.,.],[.,[.,.]]]],.],.] => [5,4,2,3,1,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19
[[[[],[[],[]],[]]]] => [[[.,[[.,[.,.]],[.,.]]],.],.] => [5,3,2,4,1,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20
[[[[],[[[]]],[]]]] => [[[.,[[[.,.],.],[.,.]]],.],.] => [5,2,3,4,1,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21
[[[[],[[],[],[]]]]] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 21
[[[[],[[[],[]]]]]] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 23
[[[[],[[[[]]]]]]] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 24
[[[[[]],[],[],[]]]] => [[[[.,.],[.,[.,[.,.]]]],.],.] => [5,4,3,1,2,6,7] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => 19
[[[[[]],[[],[]]]]] => [[[[.,.],[[.,[.,.]],.]],.],.] => [4,3,5,1,2,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 21
[[[[[],[]],[],[]]]] => [[[[.,[.,.]],[.,[.,.]]],.],.] => [5,4,2,1,3,6,7] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => 20
[[[[[[]]],[],[]]]] => [[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => 21
[[[[[],[]],[[]]]]] => [[[[.,[.,.]],[[.,.],.]],.],.] => [4,5,2,1,3,6,7] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => 21
[[[[[],[],[]],[]]]] => [[[[.,[.,[.,.]]],[.,.]],.],.] => [5,3,2,1,4,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => 21
[[[[[[],[]]],[]]]] => [[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => 23
[[[[[[[]]]],[]]]] => [[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => 24
[[[[[],[],[],[]]]]] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => 22
[[[[[],[],[[]]]]]] => [[[[.,[.,[[.,.],.]]],.],.],.] => [3,4,2,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23
[[[[[],[[]],[]]]]] => [[[[.,[[.,.],[.,.]]],.],.],.] => [4,2,3,1,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23
[[[[[],[[],[]]]]]] => [[[[.,[[.,[.,.]],.]],.],.],.] => [3,2,4,1,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 24
[[[[[[]],[],[]]]]] => [[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => 23
[[[[[[],[]],[]]]]] => [[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => 24
[[[[[[],[],[]]]]]] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => 25
[[[[[[[],[]]]]]]] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => 27
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Description
The number of relations in a poset.
This is the number of intervals $x,y$ with $x\leq y$ in the poset, and therefore the dimension of the posets incidence algebra.
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 $t$.
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.