Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

Let $[x]$ denote the greatest integer function, and let $m$ and $n$ respectively be the numbers of the points where the function $f(x) = [x] + |x - 2|$, $-2 < x < 3$, is not continuous and not differentiable. Then $m + n$ is equal to: