Identifier
Mp00011: Binary trees —to graph⟶ Graphs
Mp00324: Graphs —chromatic difference sequence⟶ Integer compositions
Images
[.,.] => ([],1) => [1]
[.,[.,.]] => ([(0,1)],2) => [1,1]
[[.,.],.] => ([(0,1)],2) => [1,1]
[.,[.,[.,.]]] => ([(0,2),(1,2)],3) => [2,1]
[.,[[.,.],.]] => ([(0,2),(1,2)],3) => [2,1]
[[.,.],[.,.]] => ([(0,2),(1,2)],3) => [2,1]
[[.,[.,.]],.] => ([(0,2),(1,2)],3) => [2,1]
[[[.,.],.],.] => ([(0,2),(1,2)],3) => [2,1]
[.,[.,[.,[.,.]]]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[.,[.,[[.,.],.]]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[.,[[.,.],[.,.]]] => ([(0,3),(1,3),(2,3)],4) => [3,1]
[.,[[.,[.,.]],.]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[.,[[[.,.],.],.]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[.,.],[.,[.,.]]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[.,.],[[.,.],.]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[.,[.,.]],[.,.]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[[.,.],.],[.,.]] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[.,[.,[.,.]]],.] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[.,[[.,.],.]],.] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[[.,.],[.,.]],.] => ([(0,3),(1,3),(2,3)],4) => [3,1]
[[[.,[.,.]],.],.] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[[[[.,.],.],.],.] => ([(0,3),(1,2),(2,3)],4) => [2,2]
[.,[.,[.,[.,[.,.]]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[.,[.,[[.,.],.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[.,[[.,.],[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[.,[[.,[.,.]],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[.,[[[.,.],.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[[.,.],[.,[.,.]]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[[.,.],[[.,.],.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[[.,[.,.]],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[[[.,.],.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[[.,[.,[.,.]]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[[.,[[.,.],.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[[[.,.],[.,.]],.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[.,[[[.,[.,.]],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[[[[.,.],.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,.],[.,[.,[.,.]]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,.],[.,[[.,.],.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,.],[[.,.],[.,.]]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[.,.],[[.,[.,.]],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,.],[[[.,.],.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[.,.]],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[.,.]],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[.,.],.],[.,[.,.]]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[.,.],.],[[.,.],.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[.,[.,.]]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[[.,.],.]],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[.,.],[.,.]],[.,.]] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[.,[.,.]],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[[.,.],.],.],[.,.]] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[.,[.,[.,.]]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[.,[[.,.],.]]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[[.,.],[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[.,[[.,[.,.]],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[.,[[[.,.],.],.]],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[.,.],[.,[.,.]]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[.,.],[[.,.],.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[.,[.,.]],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[[.,.],.],[.,.]],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[.,[.,[.,.]]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[.,[[.,.],.]],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[[.,.],[.,.]],.],.] => ([(0,4),(1,4),(2,3),(3,4)],5) => [3,2]
[[[[.,[.,.]],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[[[[[.,.],.],.],.],.] => ([(0,4),(1,3),(2,3),(2,4)],5) => [3,2]
[.,[.,[.,[.,[.,[.,.]]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[.,[.,[[.,.],.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[.,[[.,.],[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[.,[.,[[.,[.,.]],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[.,[[[.,.],.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[[.,.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[.,[[.,.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[.,[[.,[.,.]],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[.,[[[.,.],.],[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[.,[[.,[.,[.,.]]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[[.,[[.,.],.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[[[.,.],[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[.,[[[.,[.,.]],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[[[[.,.],.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[.,.],[.,[.,[.,.]]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,.],[.,[[.,.],.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,.],[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [4,2]
[.,[[.,.],[[.,[.,.]],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,.],[[[.,.],.],.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[.,[.,[.,.]]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,[[.,.],.]],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[[.,.],[.,.]],[.,.]]] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [4,2]
[.,[[[.,[.,.]],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[[[.,.],.],.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,[.,[.,[.,.]]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[.,[.,[[.,.],.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[.,[[.,.],[.,.]]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[.,[[.,[.,.]],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[.,[[[.,.],.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[[.,.],[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[[.,.],[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[[.,[.,.]],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[.,[[[[.,.],.],[.,.]],.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
>>> Load all 625 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[[.,[[.,.],.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[[[.,.],[.,.]],.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[.,[[[[.,[.,.]],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[[[[[.,.],.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[.,[.,[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[.,[.,[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[.,[[.,.],[.,.]]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,.],[.,[[.,[.,.]],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[.,[[[.,.],.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[[.,.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,.],[[.,.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,.],[[.,[.,.]],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,.],[[[.,.],.],[.,.]]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,.],[[.,[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[[.,[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[[[.,.],[.,.]],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,.],[[[.,[.,.]],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,.],[[[[.,.],.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,.]],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,.]],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,.]],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,[.,.]],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,.]],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],.],[.,[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],.],[.,[[.,.],.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],.],[[.,.],[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,.],.],[[.,[.,.]],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],.],[[[.,.],.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[.,.]]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[.,.]]],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[.,.],.]],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[.,.],.]],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],[.,.]],[.,[.,.]]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,.],[.,.]],[[.,.],.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,[.,.]],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,[.,.]],.],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[.,.],.],.],[.,[.,.]]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[.,.],.],.],[[.,.],.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[.,[.,.]]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[[.,.],.]]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[.,.],[.,.]]],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,[[.,[.,.]],.]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[[.,.],.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[.,.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[.,[.,.]],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,.],.],[.,.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[.,[.,[.,.]]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,[[.,.],.]],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[.,.],[.,.]],.],[.,.]] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[[.,[.,.]],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[[.,.],.],.],.],[.,.]] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[.,[.,[.,.]]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[.,[[.,.],.]]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[[.,.],[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,[.,[[.,[.,.]],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[.,[[[.,.],.],.]]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[.,.],[.,[.,.]]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,[[.,.],[[.,.],.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,[[.,[.,.]],[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,[[[.,.],.],[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[.,[[.,[.,[.,.]]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[.,[[.,.],.]],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[[.,.],[.,.]],.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[.,[[[.,[.,.]],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[.,[[[[.,.],.],.],.]],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,.],[.,[.,[.,.]]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,.],[.,[[.,.],.]]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,.],[[.,.],[.,.]]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [4,2]
[[[.,.],[[.,[.,.]],.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,.],[[[.,.],.],.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,[.,.]],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[.,[.,.]],[[.,.],.]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,.],.],[.,[.,.]]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,.],.],[[.,.],.]],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[.,[.,[.,.]]],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,[[.,.],.]],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[[.,.],[.,.]],[.,.]],.] => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6) => [4,2]
[[[[.,[.,.]],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[[[.,.],.],.],[.,.]],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,[.,[.,[.,.]]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,[.,[[.,.],.]]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,[[.,.],[.,.]]],.],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[.,[[.,[.,.]],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[.,[[[.,.],.],.]],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[.,.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,.],[[.,.],.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,[.,.]],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[[.,.],.],[.,.]],.],.] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => [3,3]
[[[[.,[.,[.,.]]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[.,[[.,.],.]],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[[.,.],[.,.]],.],.],.] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => [4,2]
[[[[[.,[.,.]],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[[[[[[.,.],.],.],.],.],.] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => [3,3]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[.,[[[.,.],.],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[.,[[.,.],[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[.,[[.,[.,.]],[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[.,[[[.,.],.],[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[[.,[[.,.],.]],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[[[.,.],[.,.]],.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[.,[.,[[[.,[.,.]],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[.,[[[[.,.],.],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,.],[.,[[.,.],.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,.],[[.,.],[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[.,[[.,.],[[.,[.,.]],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,.],[[[.,.],.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[.,[[[.,.],.],[.,[.,.]]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[.,[[[.,.],.],[[.,.],.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[.,[[.,[.,[.,.]]],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,[[.,.],.]],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[.,.],[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[.,[[[.,[.,.]],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[[.,.],.],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[.,[.,[[.,.],.]]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[.,[[.,.],[.,.]]],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[.,[[.,[[.,[.,.]],.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[.,[[[.,.],.],.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[[.,.],[.,[.,.]]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[.,.],[[.,.],.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[.,[.,.]],[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[[.,.],.],[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[.,[[[.,[.,[.,.]]],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[[.,[[.,.],.]],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[[[.,.],[.,.]],.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[.,[[[[.,[.,.]],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[.,[[[[[.,.],.],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[.,[.,[[.,.],.]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[.,[[.,.],[.,[[.,[.,.]],.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[.,[[[.,.],.],.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[[.,.],[.,[.,.]]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[.,.],[[.,.],[[.,.],.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[.,.],[[.,[.,.]],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[.,.],[[[.,.],.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[.,.],[[.,[.,[.,.]]],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[[.,[[.,.],.]],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[.,[[.,.],[[[.,[.,.]],.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,.],[[[[.,.],.],.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,.]],[.,[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,.]],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[.,[.,.]],[[.,[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,.]],[[[.,.],.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],.],[.,[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],.],[.,[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,.],.],[[.,[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],.],[[[.,.],.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,[.,.]]],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[.,.],.]],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[.,.],.]],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],[.,.]],[.,[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,.],[.,.]],[[.,.],.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,[.,.]],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,[.,.]],.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,.],.],.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,.],.],.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[.,[[.,.],.]]],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[[.,.],[.,.]]],[.,.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[.,[[.,[[.,[.,.]],.]],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[[[.,.],.],.]],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[.,.],[.,[.,.]]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,.],[[.,.],.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,[.,.]],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[[.,.],.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,[.,[.,.]]],.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[.,[[.,.],.]],.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[[.,.],[.,.]],.],[.,.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[.,[[[[.,[.,.]],.],.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[[[.,.],.],.],.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[.,[.,[[.,.],.]]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[.,[[.,.],[.,.]]]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[.,[[.,[.,.]],.]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[.,[[[.,.],.],.]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[[.,.],[.,[.,.]]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[.,.],[[.,.],.]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[.,[.,.]],[.,.]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[[.,.],.],[.,.]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[.,[[.,[.,[.,.]]],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[[.,[[.,.],.]],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[[[.,.],[.,.]],.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[.,[[[.,[.,.]],.],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[.,[[[[.,.],.],.],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[.,.],[.,[.,[.,.]]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],[.,[[.,.],.]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],[[.,.],[.,.]]],.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[.,.],[[.,[.,.]],.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,.],[[[.,.],.],.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,[.,.]],[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[[[.,[.,.]],[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[[[[.,.],.],[.,[.,.]]],.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[[[[.,.],.],[[.,.],.]],.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[.,[[[.,[.,[.,.]]],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,[[.,.],.]],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,.],[.,.]],[.,.]],.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[.,[[[[.,[.,.]],.],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[[.,.],.],.],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[.,[.,[.,[.,.]]]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[.,[.,[[.,.],.]]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[.,[[.,.],[.,.]]],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[.,[[.,[.,.]],.]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[.,[[[.,.],.],.]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[[.,.],[.,[.,.]]],.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,.],[[.,.],.]],.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,[.,.]],[.,.]],.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[[.,.],.],[.,.]],.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[.,[[[[.,[.,[.,.]]],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[[.,[[.,.],.]],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[[[.,.],[.,.]],.],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[.,[[[[[.,[.,.]],.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[.,[[[[[[.,.],.],.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[.,[.,[[.,.],.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[.,[[.,.],[.,.]]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,.],[.,[.,[[.,[.,.]],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[.,[[[.,.],.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[[.,.],[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[.,[[.,.],[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[.,[[.,[.,.]],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[.,[[[.,.],.],[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[.,[[.,[.,[.,.]]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[[.,[[.,.],.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[[[.,.],[.,.]],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,.],[.,[[[.,[.,.]],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[.,[[[[.,.],.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[.,.],[.,[.,[.,.]]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,.],[.,[[.,.],.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,.],[[.,.],[.,.]]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[.,.],[[.,.],[[.,[.,.]],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,.],[[[.,.],.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,[.,.]],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,.],[[.,[.,.]],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,.],[[[.,.],.],[.,[.,.]]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,.],[[[.,.],.],[[.,.],.]]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,.],[[.,[.,[.,.]]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,[[.,.],.]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[.,.],[.,.]],[.,.]]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[.,.],[[[.,[.,.]],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[[.,.],.],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[.,[.,[.,[.,.]]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[.,[.,[[.,.],.]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[.,[[.,.],[.,.]]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,.],[[.,[[.,[.,.]],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[.,[[[.,.],.],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[[.,.],[.,[.,.]]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[.,.],[[.,.],.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[.,[.,.]],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[[.,.],.],[.,.]],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,.],[[[.,[.,[.,.]]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[[.,[[.,.],.]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[[[.,.],[.,.]],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,.],[[[[.,[.,.]],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,.],[[[[[.,.],.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[.,[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,.]],[.,[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[.,[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[[.,.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,.]],[[.,.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,.]],[[.,[.,.]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,.]],[[[.,.],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,.]],[[.,[.,[.,.]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[[.,[[.,.],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,.]],[[[.,[.,.]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,.]],[[[[.,.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[.,[.,[.,[.,.]]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[.,[.,[[.,.],.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[.,[[.,.],[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],.],[.,[[.,[.,.]],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[.,[[[.,.],.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[[.,.],[.,[.,.]]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],.],[[.,.],[[.,.],.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],.],[[.,[.,.]],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],.],[[[.,.],.],[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],.],[[.,[.,[.,.]]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[[.,[[.,.],.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[[[.,.],[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],.],[[[.,[.,.]],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],.],[[[[.,.],.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,.]]],[.,[[.,.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,.]]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,[.,.]]],[[.,[.,.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,.]]],[[[.,.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],.]],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],.]],[.,[[.,.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],.]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[.,.],.]],[[.,[.,.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],.]],[[[.,.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],[.,.]],[.,[.,[.,.]]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,.]],[.,[[.,.],.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,.]],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[[[.,.],[.,.]],[[.,[.,.]],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,.]],[[[.,.],.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,.]],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,.]],.],[.,[[.,.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,.]],.],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,.]],.],[[.,[.,.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,.]],.],[[[.,.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],.],.],[.,[.,[.,.]]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],.],.],[.,[[.,.],.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],.],.],[[.,.],[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,.],.],.],[[.,[.,.]],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],.],.],[[[.,.],.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[.,.]]]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[.,.]]]],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[.,.],.]]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[.,.],.]]],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],[.,.]]],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[.,.],[.,.]]],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[.,[.,.]],.]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,[.,.]],.]],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[.,.],.],.]],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[.,.],.],.]],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],[.,[.,.]]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[.,[.,.]]],[[.,.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[[.,.],.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[[.,.],.]],[[.,.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[.,.]],[[.,.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[.,.]],[.,[.,.]]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[.,.]],[[.,.],.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,[.,.]]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,[.,.]]],.],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[.,.],.]],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[.,.],.]],.],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],[.,.]],.],[.,[.,.]]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,.],[.,.]],.],[[.,.],.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,[.,.]],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,[.,.]],.],.],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[.,.],.],.],.],[.,[.,.]]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[.,.],.],.],.],[[.,.],.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[[.,.],.]]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[.,.],[.,.]]]],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,[[.,[.,.]],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[[.,.],.],.]]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,.],[[.,.],.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,[.,.]],[.,.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[.,.],.],[.,.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,[.,[.,.]]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,[[.,.],.]],.]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[.,.],[.,.]],.]],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[[.,[.,.]],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[[.,.],.],.],.]],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],[.,[.,[.,.]]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[.,[[.,.],.]]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[[.,.],[.,.]]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,.],[[.,[.,.]],.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,.],[[[.,.],.],.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[.,[.,.]],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[.,.],.],[.,[.,.]]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[.,.],.],[[.,.],.]],[.,.]] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[.,[.,[.,.]]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,.],.]],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[.,.]],[.,.]],[.,.]] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,.]],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],.],.],[.,.]],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,[.,[.,.]]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,[[.,.],.]]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[.,.],[.,.]]],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[[.,[.,.]],.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[[.,.],.],.]],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],[.,[.,.]]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[[.,.],.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[.,.]],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],.],[.,.]],.],[.,.]] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[.,[.,.]]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,[[.,.],.]],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[.,.],[.,.]],.],.],[.,.]] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[[.,[.,.]],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[[.,.],.],.],.],.],[.,.]] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[.,[[.,.],.]]]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[[.,.],[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,[.,[[.,[.,.]],.]]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[.,[[[.,.],.],.]]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[.,.],[.,[.,.]]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,[[.,.],[[.,.],.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,[[.,[.,.]],[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,[[[.,.],.],[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[.,[[.,[.,[.,.]]],.]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[.,[[.,.],.]],.]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[[.,.],[.,.]],.]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[.,[[[.,[.,.]],.],.]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[.,[[[[.,.],.],.],.]]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,.],[.,[.,[.,.]]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,.],[.,[[.,.],.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,.],[[.,.],[.,.]]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[.,[[.,.],[[.,[.,.]],.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,.],[[[.,.],.],.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,[.,.]],[.,[.,.]]]],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,[[.,[.,.]],[[.,.],.]]],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,[[[.,.],.],[.,[.,.]]]],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,[[[.,.],.],[[.,.],.]]],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[.,[[.,[.,[.,.]]],[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,[[.,.],.]],[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[.,.],[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[.,[[[.,[.,.]],.],[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[[.,.],.],.],[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[.,[.,[.,[.,.]]]],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,[.,[[.,.],.]]],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,[[.,.],[.,.]]],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[.,[[.,[.,.]],.]],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[.,[[[.,.],.],.]],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[.,.],[.,[.,.]]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[.,.],[[.,.],.]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[.,[.,.]],[.,.]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[[.,.],.],[.,.]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[.,[[[.,[.,[.,.]]],.],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[.,[[.,.],.]],.],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[[.,.],[.,.]],.],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[.,[[[[.,[.,.]],.],.],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[.,[[[[[.,.],.],.],.],.]],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,.],[.,[.,[.,[.,.]]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,[.,[[.,.],.]]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,[[.,.],[.,.]]]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[[[.,.],[.,[[.,[.,.]],.]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[.,[[[.,.],.],.]]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[[.,.],[.,[.,.]]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,.],[[.,.],[[.,.],.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,.],[[.,[.,.]],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,.],[[[.,.],.],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,.],[[.,[.,[.,.]]],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[[.,[[.,.],.]],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[[[.,.],[.,.]],.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[[[.,.],[[[.,[.,.]],.],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,.],[[[[.,.],.],.],.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,.]],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[.,[[.,.],.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[[.,.],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[.,[.,.]],[[.,[.,.]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,.]],[[[.,.],.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[.,[.,[.,.]]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[.,[[.,.],.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[[.,.],[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,.],.],[[.,[.,.]],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],.],[[[.,.],.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,[.,.]]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,[.,.]]],[[.,.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,.],.]],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,.],.]],[[.,.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[.,.]],[.,[.,.]]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,.],[.,.]],[[.,.],.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,.]],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[.,.]],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],.],.],[.,[.,.]]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],.],.],[[.,.],.]],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[.,[.,[.,.]]]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,[[.,.],.]]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[[.,.],[.,.]]],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[[[.,[[.,[.,.]],.]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[[[.,.],.],.]],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,.],[.,[.,.]]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,.],[[.,.],.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,.]],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[[.,.],.],[.,.]],[.,.]],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,[.,.]]],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,[[.,.],.]],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[[.,.],[.,.]],.],[.,.]],.] => ([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) => [5,2]
[[[[[.,[.,.]],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[[[.,.],.],.],.],[.,.]],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,[.,[.,[.,.]]]]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,[.,[[.,.],.]]]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,[[.,.],[.,.]]]],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[.,[[.,[.,.]],.]]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[.,[[[.,.],.],.]]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[.,.],[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,.],[[.,.],.]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,[.,.]],[.,.]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[[.,.],.],[.,.]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[.,[[.,[.,[.,.]]],.]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[.,[[.,.],.]],.]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[[.,.],[.,.]],.]],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[.,[[[.,[.,.]],.],.]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[.,[[[[.,.],.],.],.]],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,.],[.,[.,[.,.]]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[.,[[.,.],.]]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[[.,.],[.,.]]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[.,.],[[.,[.,.]],.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,.],[[[.,.],.],.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[.,.]],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,.]],[[.,.],.]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[[.,.],.],[.,[.,.]]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[[.,.],.],[[.,.],.]],.],.] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) => [4,3]
[[[[.,[.,[.,.]]],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[[.,.],.]],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],[.,.]],[.,.]],.],.] => ([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) => [4,3]
[[[[[.,[.,.]],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[[.,.],.],.],[.,.]],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[.,[.,[.,[.,.]]]],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,[.,[[.,.],.]]],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,[[.,.],[.,.]]],.],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[.,[[.,[.,.]],.]],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[.,[[[.,.],.],.]],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[.,.],[.,[.,.]]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,.],[[.,.],.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,[.,.]],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[[.,.],.],[.,.]],.],.],.] => ([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) => [4,3]
[[[[[.,[.,[.,.]]],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[.,[[.,.],.]],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[[.,.],[.,.]],.],.],.],.] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) => [4,3]
[[[[[[.,[.,.]],.],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
[[[[[[[.,.],.],.],.],.],.],.] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => [4,3]
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.
Map
chromatic difference sequence
Description
The chromatic difference sequence of a graph.
Let $G$ be a simple graph with chromatic number $\kappa$. Let $\alpha_m$ be the maximum number of vertices in a $m$-colorable subgraph of $G$. Set $\delta_m=\alpha_m-\alpha_{m-1}$. The sequence $\delta_1,\delta_2,\dots\delta_\kappa$ is the chromatic difference sequence of $G$.
All entries of the chromatic difference sequence are positive: $\alpha_m > \alpha_{m-1}$ for $m < \kappa$, because we can assign any uncolored vertex of a partial coloring with $m-1$ colors the color $m$. Therefore, the chromatic difference sequence is a composition of the number of vertices of $G$ into $\kappa$ parts.