Easy# Maximal Cardinality of the Generating Set of a Ring

ABSALG-KTMHYI

Let $S$ be a subset of ring $R$. We say $S$ *generates* $R$ if every element of $R$ can be obtained from finite sums and products of elements in $S$.

If $R = \mathbb{Z}/n\mathbb{Z}$, where $n$ is even, what is the maximum cardinality of $S$?