Let $f: (-2, 2) \rightarrow \mathbb{R}$ be defined by $f(x) = \begin{cases} x\lfloor x\rfloor, & 0 \leq x < 2 \\ (x-1)\lfloor x\rfloor, & -2 < x < 0 \end{cases}$ where $\lfloor x \rfloor$ denotes the greatest integer function. If $m$ and $n$ respectively are the number of points in $(-2, 2)$ at which $y = f(x)$ is not continuous and not differentiable, then $m + n$ is equal to $\_\_\_\_$.