Consider the function $ f(x)= \begin{cases} \dfrac{a\,(7x-12-x^{2})}{\,b\,\lfloor x^{2}-7x+12\rfloor\,}, & x<3,\\[6pt] \dfrac{\sin(x-3)}{2^{\,x-1}}, & x>3,\\[6pt] b, & x=3, \end{cases} $ where $\lfloor x\rfloor$ denotes the greatest integer $\le x$. 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: