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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


Combinatorics

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First Solve @rahmanistiyak6

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