HMMT 2018 T6

Let $n \geq 2$ be a positive integer. A subset of positive integers $S$ is said to be comprehensive if for every integer $0 \leq x<n$, there is a subset of $S$ whose sum has remainder $x$ when divided by $n$. Note that the empty set has sum 0 . Show that if a set $S$ is comprehensive, then there is some (not necessarily proper) subset of $S$ with at most $n-1$ elements which is also comprehensive.