JBMO-SL 2018 A7

Let $A$ be a set of positive integers with the following properties:

(a) If $n$ is an element of $A$ then $n \leqslant 2018$.

(b) If $S$ is a subset of $A$ with $|S|=3$ then there are two elements $n, m$ of $S$ with $|n-m| \geqslant \sqrt{n}+\sqrt{m}$.

What is the maximum number of elements that $A$ can have?