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.

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