Erdős Problem #957 — Product of the extreme-distance multiplicities

Let $A$ be a set of $n$ distinct points in $\mathbb{R}^2$. If $s_{\min}$ and $s_{\max}$ are the numbers of unordered pairs of points attaining respectively the smallest and largest distances determined by $A$, is $s_{\min}s_{\max}\leq(9/8+o(1))n^2$?