BALKAN 1994 Problem 3

Let $a_1,a_2,\ldots,a_n$ be a permutation of the numbers $1,2,\ldots,n$ , with $n\geq 2$ . Determine the largest possible value of the sum $$S(n)=|a_2-a_1|+ |a_3-a_2| + \cdots + |a_n-a_{n-1}| .$$ Romania