Consider a function $\vec{f}=\frac{1}{r^{2}} \hat{r}$ where $r$ is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of this function over a sphere of radius $R$, which includes the origin, is
1. $0$
2. $2 \pi$
3. $4 \pi$
4. $R \pi$