Identifier
Mp00047: Ordered trees —to poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
Images
[] => ([],1) => ([],1) => ([],1)
[[]] => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2)
[[],[]] => ([(0,2),(1,2)],3) => ([(0,1),(0,2)],3) => ([],1)
[[[]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3)],4) => ([],1)
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => ([(0,1)],2)
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(0,3),(3,1)],4) => ([(0,1)],2)
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(3,1),(3,2)],4) => ([],1)
[[[[]]]] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[],[]] => ([(0,4),(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(0,4)],5) => ([],1)
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => ([(0,1)],2)
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => ([(0,1)],2)
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => ([],1)
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,2),(2,1)],3)
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(0,3),(0,4),(4,1)],5) => ([(0,1)],2)
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,3),(0,4),(3,2),(4,1)],5) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,3),(0,4),(4,1),(4,2)],5) => ([],1)
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(0,4),(3,1),(4,3)],5) => ([(0,2),(2,1)],3)
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,4),(4,1),(4,2),(4,3)],5) => ([],1)
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => ([(0,1)],2)
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,4),(3,2),(4,1),(4,3)],5) => ([(0,1)],2)
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(3,4),(4,1),(4,2)],5) => ([],1)
[[[[[]]]]] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[],[],[],[]] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => ([],1)
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => ([(0,1)],2)
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => ([(0,1)],2)
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => ([],1)
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3)
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => ([(0,1)],2)
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => ([],1)
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3)
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => ([],1)
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => ([(0,1)],2)
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => ([(0,1)],2)
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => ([],1)
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,3),(2,1),(3,2)],4)
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => ([(0,1)],2)
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => ([(0,1)],2)
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => ([],1)
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3)
[[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6) => ([(0,1)],2)
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6) => ([],1)
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => ([(0,1)],2)
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6) => ([(0,1)],2)
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6) => ([],1)
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[],[]]] => ([(0,5),(1,5),(2,5),(3,5),(5,4)],6) => ([(0,5),(5,1),(5,2),(5,3),(5,4)],6) => ([],1)
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => ([(0,1)],2)
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => ([(0,1)],2)
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => ([],1)
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3)
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,5),(4,3),(5,1),(5,2),(5,4)],6) => ([(0,1)],2)
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,5),(4,2),(4,3),(5,1),(5,4)],6) => ([],1)
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3)
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(0,4),(4,5),(5,1),(5,2),(5,3)],6) => ([],1)
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => ([(0,1)],2)
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(3,2),(4,5),(5,1),(5,3)],6) => ([(0,1)],2)
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(3,5),(4,3),(5,1),(5,2)],6) => ([],1)
[[[[[[]]]]]] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7) => ([],1)
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => ([(0,1)],2)
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => ([(0,1)],2)
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => ([],1)
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => ([(0,2),(2,1)],3)
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => ([(0,1)],2)
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => ([],1)
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => ([(0,2),(2,1)],3)
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[],[],[[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[],[],[[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => ([],1)
[[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => ([(0,3),(2,1),(3,2)],4)
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => ([(0,1)],2)
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => ([],1)
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => ([(0,2),(2,1)],3)
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[],[[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[],[[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => ([],1)
[[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => ([],1)
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[],[[],[[],[]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
[[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => ([(0,2),(2,1)],3)
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[[],[]],[]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
>>> Load all 301 entries. <<<
[[],[[[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => ([(0,2),(2,1)],3)
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[],[[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => ([(0,1)],2)
[[],[[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => ([(0,1)],2)
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7) => ([],1)
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[]],[],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7) => ([(0,1)],2)
[[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[[]],[],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(5,2),(6,1)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(4,3),(5,2),(6,1)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8)
[[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[[]],[[[]]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => ([(0,1)],2)
[[[]],[[],[[]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[[]],[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7) => ([(0,1)],2)
[[[]],[[[[]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7) => ([],1)
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7) => ([(0,2),(2,1)],3)
[[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[[[]]],[],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,4),(0,5),(0,6),(5,3),(6,1),(6,2)],7) => ([(0,1)],2)
[[[[]]],[[]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[]],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => ([(0,5),(0,6),(5,3),(5,4),(6,1),(6,2)],7) => ([],1)
[[[],[]],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7) => ([(0,2),(2,1)],3)
[[[[]]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7) => ([(0,2),(2,1)],3)
[[[[]]],[[[]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[[],[[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[[[]],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7) => ([(0,1)],2)
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7) => ([],1)
[[[[[]]]],[],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,5),(0,6),(5,4),(6,1),(6,2),(6,3)],7) => ([(0,1)],2)
[[[],[[]]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[]],[]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[],[]]],[[]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7) => ([(0,1)],2)
[[[[[]]]],[[]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7) => ([],1)
[[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[[],[[],[]]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
[[[],[[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => ([(0,2),(2,1)],3)
[[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7) => ([(0,1)],2)
[[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[],[]],[]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
[[[[[]]],[]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7) => ([(0,2),(2,1)],3)
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[[[],[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => ([(0,1)],2)
[[[[[]],[]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7) => ([(0,1)],2)
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7) => ([],1)
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) => ([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7) => ([],1)
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => ([(0,1)],2)
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => ([(0,1)],2)
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => ([],1)
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7) => ([(0,2),(2,1)],3)
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => ([(0,1)],2)
[[[],[[]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => ([],1)
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7) => ([(0,2),(2,1)],3)
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[[],[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => ([(0,1)],2)
[[[],[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => ([(0,1)],2)
[[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => ([],1)
[[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7) => ([(0,1)],2)
[[[[]],[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[]],[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,6),(4,3),(5,2),(6,1),(6,4),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[]],[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7) => ([(0,1)],2)
[[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7) => ([],1)
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7) => ([(0,2),(2,1)],3)
[[[[],[]],[[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,6),(4,3),(5,1),(5,2),(6,4),(6,5)],7) => ([(0,1)],2)
[[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7) => ([],1)
[[[[],[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => ([(0,1)],2)
[[[[[]],[]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7) => ([(0,1)],2)
[[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7) => ([],1)
[[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) => ([(0,3),(2,1),(3,2)],4)
[[[[],[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) => ([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7) => ([],1)
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => ([(0,1)],2)
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => ([(0,1)],2)
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
[[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => ([(0,2),(2,1)],3)
[[[[[]],[],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7) => ([(0,1)],2)
[[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7) => ([],1)
[[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) => ([(0,2),(2,1)],3)
[[[[[],[],[]]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) => ([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7) => ([],1)
[[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => ([(0,1)],2)
[[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) => ([(0,1)],2)
[[[[[[],[]]]]]] => ([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) => ([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) => ([],1)
[[[[[[[]]]]]]] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[],[],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8) => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7)],8) => ([],1)
[[],[],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[],[],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[],[],[],[],[[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8) => ([(0,2),(2,1)],3)
[[],[],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[],[],[],[[]],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[],[],[[[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8) => ([(0,2),(2,1)],3)
[[],[],[],[[[[]]]]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[],[],[[]],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[],[[]],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[],[[]],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[],[[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8) => ([(0,2),(2,1)],3)
[[],[],[[[]]],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[],[[[[]]]],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8) => ([(0,3),(2,1),(3,2)],4)
[[],[[]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[],[[]],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[]],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[]],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[]],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[],[[]],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[]],[[[[]]]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[],[[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8) => ([(0,2),(2,1)],3)
[[],[[[]]],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[[]]],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[],[[],[]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,5),(0,6),(0,7),(6,3),(6,4),(7,1),(7,2)],8) => ([],1)
[[],[[],[]],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[],[[[]]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[],[[[]]],[[[]]]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[[],[[[[]]]],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8) => ([(0,3),(2,1),(3,2)],4)
[[],[[[[]]]],[[]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[],[[],[[],[[]]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[],[[],[[[]],[]]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[],[[],[[[[]]]]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8) => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[],[[[],[[]]],[]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[],[[[[]],[]],[]]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[],[[[[[]]]],[]]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8) => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[],[[[[[[]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[]],[],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(7,1)],8) => ([(0,1)],2)
[[[]],[],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[]],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[]],[],[[[[]]]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[]],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,5),(0,6),(0,7),(6,2),(7,1)],8) => ([(0,1),(0,2),(1,3),(2,3)],4)
[[[]],[[[]]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[]],[[[[]]]],[]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[]],[[[[[]]]]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[[[[]]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(0,3),(0,4),(0,5),(0,7),(6,1),(7,6)],8) => ([(0,2),(2,1)],3)
[[[[]]],[],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[[]]],[],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,5),(0,6),(0,7),(6,3),(6,4),(7,1),(7,2)],8) => ([],1)
[[[],[]],[],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[[[]]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[[[]]],[],[[[]]]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[[[[]]],[[]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(0,6),(0,7),(5,1),(6,2),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
[[[],[]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,5),(0,6),(0,7),(6,3),(6,4),(7,1),(7,2)],8) => ([],1)
[[[],[]],[[[]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[[[]]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,4),(0,6),(0,7),(5,3),(6,5),(7,1),(7,2)],8) => ([(0,2),(2,1)],3)
[[[[]]],[[[]]],[]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,3),(0,6),(0,7),(4,2),(5,1),(6,4),(7,5)],8) => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
[[[],[]],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,6),(0,7),(4,5),(5,3),(6,4),(7,1),(7,2)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[]]],[[[[]]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[[[[[]]]],[],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,2),(0,3),(0,4),(0,7),(5,6),(6,1),(7,5)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]]],[],[[]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[[[]]]],[[]],[]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,6),(0,7),(4,5),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
[[[[[]]]],[[],[]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,6),(0,7),(4,5),(5,3),(6,4),(7,1),(7,2)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]]],[[[]]]] => ([(0,5),(1,6),(2,7),(3,7),(4,3),(5,4),(6,2)],8) => ([(0,6),(0,7),(3,4),(4,1),(5,2),(6,5),(7,3)],8) => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
[[[[[[]]]]],[[]]] => ([(0,6),(1,3),(2,7),(3,7),(4,5),(5,2),(6,4)],8) => ([(0,6),(0,7),(3,5),(4,3),(5,2),(6,4),(7,1)],8) => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
[[[],[[],[[]]]],[]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[[],[[[]],[]]],[]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[[],[[[[]]]]],[]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8) => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[],[[]]],[]],[]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[[[[]],[]],[]],[]] => ([(0,6),(1,7),(2,5),(3,4),(4,7),(5,6),(7,5)],8) => ([(0,4),(0,7),(5,3),(6,2),(6,5),(7,1),(7,6)],8) => ([(0,1)],2)
[[[[[[]]]],[]],[]] => ([(0,7),(1,3),(2,6),(3,5),(4,7),(5,4),(7,6)],8) => ([(0,3),(0,7),(4,6),(5,2),(6,5),(7,1),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[[[]]]]]],[]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,2),(0,7),(3,4),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[],[],[],[[[]]]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8) => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8) => ([(0,2),(2,1)],3)
[[[],[],[[[]]],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8) => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8) => ([(0,2),(2,1)],3)
[[[],[],[[[[]]]]]] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8) => ([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[],[[[]]],[],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8) => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8) => ([(0,2),(2,1)],3)
[[[],[[[[]]]],[]]] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8) => ([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]],[],[],[]]] => ([(0,7),(1,7),(2,7),(3,4),(4,6),(6,7),(7,5)],8) => ([(0,7),(5,6),(6,4),(7,1),(7,2),(7,3),(7,5)],8) => ([(0,2),(2,1)],3)
[[[[[[]]]],[],[]]] => ([(0,7),(1,7),(2,6),(3,7),(5,3),(6,5),(7,4)],8) => ([(0,7),(4,6),(5,3),(6,5),(7,1),(7,2),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[],[[[[]]]]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8) => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[[[]]]],[]]]] => ([(0,7),(1,5),(3,7),(4,3),(5,4),(6,2),(7,6)],8) => ([(0,6),(3,5),(4,3),(5,1),(6,7),(7,2),(7,4)],8) => ([(0,3),(2,1),(3,2)],4)
[[[[[],[],[],[]]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,6),(6,5),(7,4)],8) => ([(0,6),(5,7),(6,5),(7,1),(7,2),(7,3),(7,4)],8) => ([],1)
[[[[[[[[]]]]]]]] => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[[]],[[[[[[]]]]]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[[[[]]],[[[[[]]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[[[[[]]]],[[[[]]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,2),(5,3),(6,4),(7,5)],9) => ([(0,7),(0,8),(3,5),(4,6),(5,2),(6,1),(7,3),(8,4)],9) => ([(0,5),(0,6),(1,4),(1,15),(2,3),(2,14),(3,8),(4,9),(5,2),(5,13),(6,1),(6,13),(8,10),(9,11),(10,7),(11,7),(12,10),(12,11),(13,14),(13,15),(14,8),(14,12),(15,9),(15,12)],16)
[[[[[[]]]]],[[[]]]] => ([(0,7),(1,6),(2,8),(3,8),(4,5),(5,3),(6,4),(7,2)],9) => ([(0,7),(0,8),(3,5),(4,3),(5,2),(6,1),(7,6),(8,4)],9) => ([(0,5),(0,6),(1,4),(1,14),(2,11),(3,10),(4,3),(4,12),(5,1),(5,13),(6,2),(6,13),(8,9),(9,7),(10,7),(11,8),(12,9),(12,10),(13,11),(13,14),(14,8),(14,12)],15)
[[[[[[[]]]]]],[[]]] => ([(0,7),(1,3),(2,8),(3,8),(4,6),(5,4),(6,2),(7,5)],9) => ([(0,7),(0,8),(3,4),(4,6),(5,3),(6,2),(7,5),(8,1)],9) => ([(0,2),(0,6),(1,8),(2,7),(3,5),(3,9),(4,3),(4,11),(5,1),(5,10),(6,4),(6,7),(7,11),(9,10),(10,8),(11,9)],12)
[[[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,2),(0,8),(3,5),(4,3),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
[[[[[[[[[]]]]]]]]] => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9)
[[[[[[[[[]]]]]]]],[]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[],[[[[[[[[]]]]]]]]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,2),(0,9),(3,4),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
[[[[[[[[[[]]]]]]]]]] => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10)
[[[]],[[[[[[[]]]]]]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10) => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
[[[[]]],[[[[[[]]]]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10) => ([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10) => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
[[[[[]]]],[[[[[]]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10) => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10) => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
[[[[[[]]]]],[[[[]]]]] => ([(0,7),(1,8),(2,9),(3,9),(4,5),(5,2),(6,3),(7,6),(8,4)],10) => ([(0,8),(0,9),(3,7),(4,3),(5,6),(6,1),(7,2),(8,4),(9,5)],10) => ([(0,6),(0,7),(1,4),(1,16),(2,5),(2,15),(3,13),(4,12),(5,3),(5,19),(6,1),(6,17),(7,2),(7,17),(9,11),(10,8),(11,8),(12,9),(13,10),(14,9),(14,18),(15,14),(15,19),(16,12),(16,14),(17,15),(17,16),(18,10),(18,11),(19,13),(19,18)],20)
[[[[[[[]]]]]],[[[]]]] => ([(0,8),(1,7),(2,9),(3,9),(4,6),(5,4),(6,3),(7,5),(8,2)],10) => ([(0,8),(0,9),(3,4),(4,6),(5,3),(6,2),(7,1),(8,7),(9,5)],10) => ([(0,6),(0,7),(1,11),(2,5),(2,15),(3,13),(4,3),(4,17),(5,4),(5,16),(6,2),(6,14),(7,1),(7,14),(9,12),(10,9),(11,10),(12,8),(13,8),(14,11),(14,15),(15,10),(15,16),(16,9),(16,17),(17,12),(17,13)],18)
[[[[[[[[]]]]]]],[[]]] => ([(0,8),(1,3),(2,9),(3,9),(4,5),(5,7),(6,4),(7,2),(8,6)],10) => ([(0,8),(0,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6),(9,1)],10) => ([(0,2),(0,7),(1,9),(2,8),(3,4),(3,11),(4,6),(4,10),(5,3),(5,13),(6,1),(6,12),(7,5),(7,8),(8,13),(10,12),(11,10),(12,9),(13,11)],14)
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.