Erdős problem 503

What is the size of the largest $A \subseteq \mathbb{R}^n$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x$, $y$, $z$ from $A$, at least two of the distances $|x - y|$, $|y - z|$, $|x - z|$ are equal.