For any finite non empty set $$X$$ of integers, let $$\max(X)$$ denote the largest element of $$X$$ and $$|X|$$ denote the number of elements in $$X$$. If $$N$$ is the number of ordered pairs $$(A, B)$$ of finite non-empty sets of positive integers, such that $$\max(A)\times|B|=12$$ and $$|A|\times\max(B)=11$$, and $$N$$ can be written as $$100a+b$$ where $$a, b$$ are positive integers less than $$100$$, find $$a+b$$.