Following is a problem, which makes use of the pigeonhole principle. But How?

"Let $A$ be a set of $n$ integers. Prove that $A$ contains a subset such that
the sum of its elements is divisible by $n$."

I found some solutions which say there are going to be $n+1$ pigeons (for partial sums) and $n$ holes (For remainders). But, are the partial sums not going to be $2^{n}-1$? (Excluding the empty subset).