HMMT 2020 T6

Let $n>1$ be a positive integer and $S$ be a collection of $\frac{1}{2}\binom{2 n}{n}$ distinct $n$-element subsets of $\{1,2, \ldots, 2 n\}$. Show that there exists $A, B \in S$ such that $|A \cap B| \leq 1$.