Piecewise Continuity with Greatest Integer

Consider the function. f(x)={

‌ a(7x−12−x2) b|x2−7x+12|	,‌x<3
2‌ sin‌(x−3) x−[x]	,‌x>3
b	,‌x=3

.
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 :