Party acquaintances

There are $n$ people at a party. Suppose they are friendly people, and each person has 8 acquaintances. Now, Bob, a passer-by notices this special property:

(i) Each pair of people who are mutually acquainted has exactly 4 common acquaintances.

(ii) Each pair of people who are mutually unacquainted has exactly 2 common acquaintances

Find the number of possible values of $n$ .

Note: If you think that there are infinitely many answers, then input your answer as 999. If you think that there are no answers, input your answer as 0.