BALKAN-SL 2009 C2

Let $A_1, A_2, \ldots , A_m$ be subsets of the set $\{ 1,2, \ldots , n \}$ , such that the cardinal of each subset $A_i$ , such $1 \le i \le m$ is not divisible by $30$ , while the cardinal of each of the subsets $A_i \cap A_j$ for $1 \le i,j \le m$ , $i \neq j$ is divisible by $30$ . Prove \begin{align*} 2m - \left \lfloor \frac{m}{30} \right \rfloor \le 3n \end{align*}