Sinthia loves Pokemon and she wants to catch them all. In Victory road, there are total of $110$ Pokemon. Sinthia wants to catch as many of them as possible. However, she can not catch any two Pokemons that are enemy to each other. After exploring around for a while, she makes the following two observation.
$1$. Every Pokemon in Victory road is enemy with with exactly two other Pokemons.
$2$. Due to her inability to catch Pokemon that are enemy, the maximum number of Pokemon that she can catch is equal to $n$.
What is the sum of all possible values of $n$.
Source: BdMO 2021