Let \(f(n)\) and \(g(n)\) be functions satisfying $$f(n) = \begin{cases}\sqrt{n} & \text{ if } \sqrt{n} \text{ is an integer}\\ 1 + f(n+1) & \text{ otherwise} \end{cases}$$and $$g(n) = \begin{cases}\sqrt{n} & \text{ if } \sqrt{n} \text{ is an integer}\\ 2 + g(n+2) & \text{ otherwise} \end{cases}$$for positive integers \(n\) Find the least positive integer \(n\) such that \(\tfrac{f(n)}{g(n)} = \tfrac{4}{7}\).