JMO 1995 Problem 1

Let $n\geq 2$ be integers and $r$ be positive integers such that $r$ is not the multiple of $n$, and let $g$ be the greatest common measure of $n$ and $r$. Prove that $$\sum_{i=1}^{n-1} \left\{\frac{ri}{n} \right\}\ =\frac{1}{2}(n-g).$$ where $\left\{x\right\}$ is the fractional part, that is to say, which means the value by subtracting $x$ from the maximum integer value which is equal or less than $x$.