Consider the function
$f(x)=\left\{\begin{array}{cl} \frac{a\left(7 x-12-x^2\right)}{b\left|x^2-7 x+12\right|} & , x<3 \\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\ b & , x=3 \end{array}\right.$
Where $[\mathrm{x}]$ denotes the greatest integer less than or equal to $x$. If $S$ denotes the set of all ordered pairs ($a, b$) such that $f(x)$ is continuous at $x=3$, then the number of elements in S is :