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 $ \displaystyle\min_{1\le i\le n-1}\left|\sigma(i+1)-\sigma(i)\right|$. Determine $ \displaystyle\max_{\sigma\in S_n}l(\sigma)$.