Continuity and Differentiability of Functions

Let $f(x)=\begin{cases} e^{x-1}, & x < 0 \\ x^{2}-5x+6, & x \ge 0 \end{cases}$ and $g(x)=f(|x|)+|f(x)|$. If the number of points where g is not continuous and is not differentiable are α and β respectively, then $\alpha+\beta$ is equal to _____.