Consider the function $$f:\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)\to(-\infty,\infty)$$ defined by

$$f(x)=(|x|+|x-1|)\sin x+[x\sin x],$$

where $$[x\sin x]$$ is the greatest integer less than or equal to $$x\sin x$$.

Let $$\alpha$$ be the total number of points in the interval $$\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)$$ at which $$f$$ is NOT continuous, and let $$\beta$$ be the total number of points in the interval $$\left(-\tfrac{\pi}{2},\tfrac{\pi}{2}\right)$$ at which $$f$$ is NOT differentiable. Then the value of $$\alpha+\beta$$ is ___.