CN-LEAGUE 2005 Problem 3

For each positive integer, define a function $$f(n)=\begin{cases}0, &\text{if n is the square of an integer} \left\lfloor\frac{1}{\{\sqrt{n}\}}\right\rfloor, &\text{if n is not the square of an integer}\end{cases}.$$ Find the value of $\sum_{k=1}^{200} f(k)$ .