Let $[ \mathrm { t } ]$ 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 $S$ be the set of all points in the interval $[ 0,8 ]$ at which $f$ is not continuous. Then $\sum _ { \mathrm { a } \in \mathrm { S } } \mathrm { a }$ is equal to $\_\_\_\_$