Unclassified (maths): JEE Main 2025 Mathematics question

Let $f(x) = \begin{cases} 3x, & x < 0 \\ \min \{1 + x + [x], x + 2[x]\}, & 0 \leq x \leq 2 \\ 5, & x > 2 \end{cases}$ where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where $f$ is not continuous and is not differentiable, respectively, then $\alpha + \beta$ equals