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 $n$?