Let $\mathrm { f } ( x ) = \left\{ \begin{array} { l l } 3 x , & x < 0 \\ \min \{ 1 + x + [ x ] , x + 2 [ x ] \} , & 0 \leq x \leq 2 \\ 5 , & x > 2 , \end{array} \right.$ 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