Let \([t]\) denote the greatest integer less than or equal to \( t \). Let \( f:[0,\infty)\to \mathbb{R} \) be a function defined by \( f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}] \). Let \( S \) be the set of all points in the interval \( [0,8] \) at which \( f \) is not continuous. Then \( \sum\limits_{a\in S} a \) is equal to ______.
