RO-TST 2008 Problem 13

Let $n$ be a nonzero positive integer. A set of persons is called a $n$ -balanced set if in any subset of $3$ persons there exists at least two which know each other and in each subset of $n$ persons there are two which don't know each other. Prove that a $n$ -balanced set has at most $(n - 1)(n + 2)/2$ persons.