Given an integer $n$ greater than $1$, suppose $x_1,x_2,\ldots,x_n$ are integers such that none of them is divisible by $n$, and neither their sum. Prove that there exists atleast $n-1$ non-empty subsets $\mathcal I\subseteq \{1,\ldots, n\}$ such that $\sum_{i\in\mathcal I}x_i$ is divisible by $n$