Let $n \geq 3$ be an integer. For a permutation $\sigma=\left(a_{1}, a_{2}, \ldots a_{n}\right)$ of $(1,2, \ldots, n)$ we let $f \sigma(x)=a_{n} x^{n-1}+a^{n-1}+\ldots+a_{2} x+a_{1} .$ Let $S \sigma$ be the sum of the roots of $f \sigma(x)=0$ and let $S$ denote the sum over all permutation $\sigma$ of $(1,2, \ldots, n)$ of the number $S_{\sigma}$. Then