DANUBE 2007 Problem 1

Let $n\ge2$ be a positive integer and denote by $S_n$ the set of all permutations of the set $\{1,2,\ldots,n\}$ . For $\sigma\in S_n$ define $l(\sigma)$ to be $\min_{1\le i\le n-1}\left|\sigma(i+1)-\sigma(i)\right|$ . Determine $\max_{\sigma\in S_n}l(\sigma)$ .