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