Mathematics Question from JEE Main 2023 · 10 April, Shift 1

Let $f(x)$ be defined as: $f(x) = x\lfloor x\rfloor$, $-2 < x < 0$, and $f(x) = (x - 1)\lfloor x\rfloor$, $0 \leq x < 2$. If $m$ and $n$ are the number of points in $(-2, 2)$ where $y = |f(x)|$ is not continuous and not differentiable, then $m + n$ is equal to: