Let ${\rm{f}}(x) = \left\{ {\begin{array}{*{20}{c}} {3x,}&{x < 0}\\ {\min \{ 1 + x + [x],x + 2[x]\} ,}&{0 \le x \le 2}\\ {5,}&{x > 2} \end{array}} \right.$
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 ___ .