Identifier
Mp00047: Ordered trees —to poset⟶ Posets
Mp00205: Posets —maximal antichains⟶ Lattices
Mp00196: Lattices —The modular quotient of a lattice.⟶ Lattices
Images
[] => ([],1) => ([],1) => ([],1)
[[]] => ([(0,1)],2) => ([(0,1)],2) => ([(0,1)],2)
[[],[]] => ([(0,2),(1,2)],3) => ([(0,1)],2) => ([(0,1)],2)
[[[]]] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[]] => ([(0,3),(1,3),(2,3)],4) => ([(0,1)],2) => ([(0,1)],2)
[[],[[]]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[]],[]] => ([(0,3),(1,2),(2,3)],4) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[]]] => ([(0,3),(1,3),(3,2)],4) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[[]]]] => ([(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)],2) => ([(0,1)],2)
[[],[],[[]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[]],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[],[]]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[[]]]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[]],[],[]] => ([(0,4),(1,4),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[]],[[]]] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[],[]],[]] => ([(0,4),(1,3),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[[]]],[]] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[]]] => ([(0,4),(1,4),(2,4),(4,3)],5) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[[]]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[]]] => ([(0,4),(1,2),(2,4),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[]]]] => ([(0,4),(1,4),(2,3),(4,2)],5) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]]]] => ([(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)],2) => ([(0,1)],2)
[[],[],[],[[]]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[]],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[],[]],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[[]]],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[],[]]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[],[[]]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[]],[]]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[],[]]]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[[]]]]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[]],[],[],[]] => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[]],[],[[]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[],[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[[]]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[],[]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[[]]],[],[]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[]],[[]]] => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[[]]],[[]]] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[],[]],[]] => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[]],[]] => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[]]],[]] => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]]],[]] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(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),(5,4)],6) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[],[[]]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[]],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[],[]]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[[]]]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[]],[],[]]] => ([(0,5),(1,5),(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[[]]]] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[],[]],[]]] => ([(0,5),(1,4),(2,4),(4,5),(5,3)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]],[]]] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[],[]]]] => ([(0,5),(1,5),(2,5),(3,4),(5,3)],6) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[[]]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[]],[]]]] => ([(0,5),(1,3),(3,5),(4,2),(5,4)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[],[]]]]] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[]]]]]] => ([(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)],2) => ([(0,1)],2)
[[],[],[],[],[[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[],[[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[],[[],[]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[],[[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[]],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[]],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[],[[],[]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[[]]],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[],[[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[]],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[],[]],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[[]]],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[]],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[[]]],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[],[]]],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[[]]]],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[],[],[],[]]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[],[[],[],[[]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[[]],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[[],[]]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[],[[[]]]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[]],[[]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[],[[[],[]],[]]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
>>> Load all 371 entries. <<<
[[],[[[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[],[]]]]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[[]]]]]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(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),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[]],[],[],[[]]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[[],[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[[[]]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[]],[[]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9) => ([(0,2),(0,3),(0,4),(2,6),(2,7),(3,5),(3,7),(4,5),(4,6),(5,8),(6,8),(7,8),(8,1)],9)
[[[]],[[],[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[[]]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[],[[]]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[[]],[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[[[]]]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[[]]],[],[],[]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[]],[],[[]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[[]]],[],[[]]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[[]],[]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[[]]],[[]],[]] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[[],[]]] => ([(0,5),(1,5),(2,4),(3,4),(4,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[],[]],[[[]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[[],[]]] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[[[]]]] => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[],[],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[]],[],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[]]],[],[]] => ([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]]],[],[]] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[],[]],[[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(6,5)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[],[[]]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]],[]],[[]]] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[],[]]],[[]]] => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[[]]]],[[]]] => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[],[],[]],[]] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[],[[]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[]],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[],[]]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[]],[],[]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[[]]],[]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[],[]],[]],[]] => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]],[]],[]] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[],[]]],[]] => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[[]]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[]],[]]],[]] => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[],[]]]],[]] => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[]]]]],[]] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(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),(6,5)],7) => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3)
[[[],[],[],[[]]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[[]],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[[],[]]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[],[[[]]]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[]],[],[]]] => ([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[]],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[],[[],[]],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[[]]],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[],[],[]]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[],[[],[[]]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[[]],[]]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[[],[]]]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[[[]]]]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(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),(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]],[],[[]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[]],[[]],[]]] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[]],[[],[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[]],[[[]]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[],[]],[],[]]] => ([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[[]]],[],[]]] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[]],[[]]]] => ([(0,5),(1,5),(2,3),(3,6),(5,6),(6,4)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[[]]],[[]]]] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[],[],[]],[]]] => ([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[[]]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[]],[]],[]]] => ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[],[]]],[]]] => ([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[]]]],[]]] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(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),(4,5),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[],[],[[]]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[[]],[]]]] => ([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[[],[]]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[[[]]]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(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),(2,3),(3,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[]],[[]]]]] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[[[[],[]],[]]]] => ([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[]]],[]]]] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(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),(3,5),(5,4),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[],[[]]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[[[[]],[]]]]] => ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) => ([(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),(3,4),(4,2),(5,3),(6,5)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[[[[[]]]]]]] => ([(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)],2) => ([(0,1)],2)
[[],[],[],[],[[[]]]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[],[[]],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[],[],[[[]]],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[],[[[[]]]]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[],[[]],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[],[[]],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[],[[]],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[],[[[]]],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[],[[[]]],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[],[[[[]]]],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[]],[],[],[[]]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[]],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[]],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[]],[[[[]]]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[],[[[]]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[],[[[]]],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[[]]],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[],[]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[],[[],[]],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[[]]],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[],[[[]]],[[[]]]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[],[[[[]]]],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[]]]],[[]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[],[[[[[[]]]]]]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(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),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[],[[]],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[],[[[]]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[],[[]],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[],[[[]]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[],[[[[]]]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[]],[[]],[],[],[]] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[]],[[[]]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[]],[[[[]]]],[]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[]]],[],[],[],[]] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4)
[[[[]]],[],[],[[]]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[],[[]],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[],[]],[],[[[]]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[],[[],[]]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[],[[[]]]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[[]]],[[]],[],[]] => ([(0,7),(1,7),(2,4),(3,5),(4,6),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
[[[],[]],[[[]]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[[],[]],[]] => ([(0,7),(1,6),(2,6),(3,4),(4,5),(5,7),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[]]],[[[]]],[]] => ([(0,7),(1,6),(2,5),(3,7),(4,7),(5,3),(6,4)],8) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[],[]],[[[[]]]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[[]]]],[],[],[]] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[]]]],[],[[]]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[[]]]],[[]],[]] => ([(0,7),(1,6),(2,4),(3,7),(4,7),(5,3),(6,5)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[[]]]],[[],[]]] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[[[[]]]]]],[]] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(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),(4,6),(6,5),(7,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[[[]]]]]]]] => ([(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)
[[],[[],[[],[[],[]]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[],[[[],[]],[]]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[],[]],[[],[]]]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[],[[[],[[],[]]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[],[]],[]],[]]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[],[[[[[[[]]]]]]]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(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),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[]],[[[],[]],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[[],[]]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[[],[]],[]],[[],[]]] => ([(0,7),(1,5),(2,5),(3,6),(4,6),(5,8),(6,7),(7,8)],9) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)
[[[],[[],[[],[]]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[],[[[],[]],[]]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[],[]],[[],[]]],[]] => ([(0,7),(1,6),(2,6),(3,5),(4,5),(5,8),(6,8),(8,7)],9) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)
[[[[],[[],[]]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[],[]],[]],[]],[]] => ([(0,5),(1,5),(2,7),(3,8),(4,6),(5,8),(7,6),(8,7)],9) => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5)
[[[[[[[[]]]]]]],[]] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(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),(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)
[[],[[],[[],[[],[[],[]]]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[[],[[[],[]],[[],[]]]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[],[[],[[[],[[],[]]],[]]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[[[],[]],[[],[[],[]]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[],[[[],[]],[[[],[]],[]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[],[[[],[[],[]]],[[],[]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[],[[[[],[]],[]],[[],[]]]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[],[[[],[[],[[],[]]]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[[[[],[]],[[],[]]],[]]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[],[[[[],[[],[]]],[]],[]]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[],[]],[[],[[],[[],[]]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[]],[[],[[[],[]],[]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[]],[[[],[]],[[],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11) => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
[[[],[]],[[[],[[],[]]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[]],[[[[],[]],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[[],[]]],[[],[[],[]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[],[[],[]]],[[[],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[[],[]],[]],[[],[[],[]]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[[],[]],[]],[[[],[]],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,8),(7,9),(8,10),(9,10)],11) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10) => ([(0,4),(0,5),(2,8),(3,7),(4,3),(4,6),(5,2),(5,6),(6,7),(6,8),(7,9),(8,9),(9,1)],10)
[[[],[[],[[],[]]]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[[[],[]],[]]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[],[]],[[],[]]],[[],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,9),(8,9),(9,10)],11) => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11) => ([(0,3),(0,4),(0,5),(2,9),(3,7),(3,8),(4,6),(4,8),(5,6),(5,7),(6,10),(7,10),(8,2),(8,10),(9,1),(10,9)],11)
[[[[],[[],[]]],[]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[[[],[]],[]],[]],[[],[]]] => ([(0,9),(1,8),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,9),(9,10)],11) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9) => ([(0,3),(0,5),(2,8),(3,6),(4,2),(4,7),(5,4),(5,6),(6,7),(7,8),(8,1)],9)
[[[],[[],[[],[[],[]]]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[],[[[],[]],[[],[]]]],[]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[[],[[[],[[],[]]],[]]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[[],[]],[[],[[],[]]]],[]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[],[]],[[[],[]],[]]],[]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[],[[],[]]],[[],[]]],[]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[[],[]],[]],[[],[]]],[]] => ([(0,8),(1,9),(2,6),(3,6),(4,7),(5,7),(6,10),(7,8),(8,10),(10,9)],11) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8)
[[[[],[[],[[],[]]]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[[[[],[]],[[],[]]],[]],[]] => ([(0,9),(1,8),(2,7),(3,7),(4,6),(5,6),(6,10),(7,10),(8,9),(10,8)],11) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)
[[[[[],[[],[]]],[]],[]],[]] => ([(0,6),(1,6),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(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),(2,8),(3,9),(4,10),(5,7),(6,10),(8,9),(9,7),(10,8)],11) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
[[],[[],[[],[[],[[],[[],[]]]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[],[[],[[[],[]],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[],[[],[[[],[[],[]]],[]]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[],[[[],[]],[[],[[],[]]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[],[[[],[]],[[[],[]],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[],[[[],[[],[]]],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[],[[[[],[]],[]],[[],[]]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[],[[[],[[],[[],[]]]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[],[[[[],[]],[[],[]]],[]]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[],[[[[],[[],[]]],[]],[]]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[[],[[[],[]],[[],[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[[],[[[],[[],[]]],[]]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[[[],[]],[[],[[],[]]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[[[],[]],[[[],[]],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[[[],[[],[]]],[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[[[[],[]],[]],[[],[]]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[],[[[[],[[],[[],[]]]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[],[[[[[],[]],[[],[]]],[]],[]]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[],[[[[[],[[],[]]],[]],[]],[]]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[],[[],[[[],[]],[[],[]]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[[],[[],[[[],[[],[]]],[]]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[],[[[],[]],[[],[[],[]]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[],[[[],[]],[[[],[]],[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[],[[[],[[],[]]],[[],[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[],[[[[],[]],[]],[[],[]]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[],[[[],[[],[[],[]]]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[],[[[[],[]],[[],[]]],[]]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[[],[[[[],[[],[]]],[]],[]]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[[],[[[],[]],[[],[]]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[[[],[[[],[[],[]]],[]]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[[[],[]],[[],[[],[]]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[[[],[]],[[[],[]],[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[[[],[[],[]]],[[],[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[[[[],[]],[]],[[],[]]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,9),(5,10),(6,11),(7,12),(8,10),(10,12),(11,9),(12,11)],13) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9) => ([(0,3),(0,6),(1,8),(3,7),(4,2),(5,4),(6,1),(6,7),(7,8),(8,5)],9)
[[[[[],[[],[[],[]]]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[[[[],[]],[[],[]]],[]],[]],[]] => ([(0,8),(1,8),(2,7),(3,7),(4,10),(5,11),(6,9),(7,12),(8,12),(10,9),(11,10),(12,11)],13) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8) => ([(0,2),(0,3),(2,7),(3,7),(4,5),(5,1),(6,4),(7,6)],8)
[[[[[[],[[],[]]],[]],[]],[]],[]] => ([(0,7),(1,7),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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),(2,9),(3,10),(4,11),(5,12),(6,8),(7,12),(9,11),(10,9),(11,8),(12,10)],13) => ([(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)
[[[[[[[[[]]]]]]]],[]] => ([(0,9),(1,8),(2,9),(3,5),(4,3),(5,7),(6,4),(7,2),(8,6)],10) => ([(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) => ([(0,8),(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),(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)
Map
to poset
Description
Return the poset obtained by interpreting the tree as the Hasse diagram of a graph.
Map
maximal antichains
Description
The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains 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 $A$.
Map
The modular quotient of a lattice.
Description
The modular quotient of a lattice.
This is the largest quotient of a lattice which is modular.