Limits Continuity And Differentiability

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 \(\sum_\limits{\text {aes }} a\) is equal to __________.