OBM 2007 Problem 6

Given real numbers $x_1 < x_2 < \ldots < x_n$ such that every real number occurs at most two times among the differences $x_j - x_i$ , $1\leq i < j \leq n$ , prove that there exists at least $\lfloor n/2\rfloor$ real numbers that occurs exactly one time among such differences.