HMMT 2015 U22

Let $A_{1}, A_{2}, \ldots, A_{2015}$ be distinct points on the unit circle with center $O$. For every two distinct integers $i, j$, let $P_{i j}$ be the midpoint of $A_{i}$ and $A_{j}$. Find the smallest possible value of

$$\sum_{1 \leq i<j \leq 2015} O P_{i j}^{2}$$