1.
Consider the function
f(x)={a(7x−12−x2)b∣x2−7x+12∣,x<32x−xsin⁡(x−3),x>3b,x=3f(x) = \begin{cases} \frac{a(7x-12-x^2)}{b|x^2-7x+12|}, & x<3 \\ 2^{x} - x\sin(x-3), & x>3 \\ b, & x=3 \end{cases}
where [x][x] denotes the greatest integer less than or equal to xx. If SS denotes the set of all ordered pairs (a,b)(a, b) such that f(x)f(x) is continuous at x=3x=3, then the number of elements in SS is: