Let $[t]$ denote the greatest integer less than or equal to $t$. Let $$f:[0, \infty) \rightarrow \mathbf{R}$$ be a function defined by $$f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]$$. Let $\mathrm{S}$ be the set of all points in the interval $[0,8]$ at which $f$ is not continuous. Then $\sum_{\text {aes }} a$ is equal to $\underline{\hspace{2cm}}$.