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 $\_\_\_\_$

Let $[x]$ denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f(x) = [x] + |x - 2|$, $-2 < x < 3$, is not continuous and not differentiable. Then $\mathrm{m} + \mathrm{n}$ is equal to:
(1) 6
(2) 8
(3) 9
(4) 7

Let $\mathrm { f } ( x ) = \left\{ \begin{array} { l l } 3 x , & x < 0 \\ \min \{ 1 + x + [ x ] , x + 2 [ x ] \} , & 0 \leq x \leq 2 \\ 5 , & x > 2 , \end{array} \right.$ where [.] denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where f is not continuous and is not differentiable, respectively, then $\alpha + \beta$ equals