For a positive integer $$n>1$$, let $$g(n)$$ denote the largest positive proper divisor of $$n$$ and $$f(n)=n-g(n)$$. For example, $$g(10)=5$$, $$f(10)=5$$ and $$g(13)=1$$, $$f(13)=12$$. Let $$N$$ be the smallest positive integer such that $$f(f(f(N)))=97$$. Find the largest integer not exceeding $$\sqrt{N}$$.