KZ-MO 1999 Problem 8

Let ${{a} _ {1}}, {{a} _ {2}}, \ldots, {{a} _ {n}}$ be permutation of numbers $1,2, \ldots, n$ , where $n \geq 2$ . Find the maximum value of the sum $$S (n) = | {{a} _ {1}} - {{a} _ {2}} | + | {{a} _ {2}} - {{a} _ {3}} | + \cdots + | {{a} _ {n-1}} - {{a} _ {n}} |.$$