KöMaL 2019 A761

Let $n \ge 3$ be a positive integer. We say that a set $S$ of positive integers is good if $|S| = n$, no element of $S$ is a multiple of $n$, and the sum of all elements of $S$ is not a multiple of $n$ either. Find, in terms of $n$, the least positive integer $d$ for which there exists a good set $S$ such that there are exactly $d$ nonempty subsets of $S$ the sum of whose elements is a multiple of $n$.