ISL 1979 Problem 63

Let the sequence $\{a_i\}$ of $n$ positive reals denote the lengths of the sides of an arbitrary $n$ -gon. Let $s=\sum_{i=1}^{n}{a_i}$ . Prove that $2\ge \sum_{i=1}^{n}{\frac{a_i}{s-a_i}}\ge \frac{n}{n-1}$ .