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