PL-OM 2025 Problem 4

A positive integer $n\geq 2$ and a set $S$ consisting of $2n$ disting positive integers smaller or equal to $n^2$ are given. Prove that there exists a positive integer $r\in \{1, 2, ..., n\}$ that can be written in the form $r=a-b$ , for $a, b\in \mathbb{S}$ in at least $3$ different ways.