Configuration of $n$ points inside rectangle

Question

Given a finite set $S$ of at least $2$ points in the Euclidean plane and $x\in S$ write $$ d_S(x)=\min_{y\in S,\, y\neq x}d(x,y) $$ and $$ d(S)=\sum_{x\in S}d_S(x) $$ Now given a rectangle (product of closed bounded intervals) $R$ in the plane and $n\geq2$: Which $S\subset R$ with $|S|=n$ maximizes $d(S)$?