RMO 2015 M6

Let $S=\{1,2,\cdots, n\}$ and let $T$ be the set of all ordered triples of subsets of $S$ , say $(A_1, A_2, A_3)$ , such that $A_1\cup A_2\cup A_3=S$ . Determine, in terms of $n$ , $$\sum_{(A_1,A_2,A_3)\in T}|A_1\cap A_2\cap A_3|$$