VN-TST 2008 Problem 3

Let an integer $n > 3$ . Denote the set $T=\{1,2, \ldots,n\}.$ A subset S of T is called wanting set if S has the property: There exists a positive integer $c$ which is not greater than $\frac {n}{2}$ such that $|s_1 - s_2|\ne c$ for every pairs of arbitrary elements $s_1,s_2\in S$ . How many does a wanting set have at most are there ?