Consider the function $$f(x) = \begin{cases} \frac{a(7x - 12 - x^2)}{b|x^2 - 7x + 12|}, & x < 3 \\ 2^{\frac{\sin(x-3)}{x - [x]}}, & x > 3 \\ b, & x = 3 \end{cases}$$, where $$[x]$$ 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 :

A

2

B

Infinitely many

C

4

D

1