CMO 2013 Problem 2

The sequence $a_{1}, a_{2}, \ldots, a_{n}$ consists of the numbers $1,2, \ldots, n$ in some order. For which positive integers $n$ is it possible that $0, a_{1}, a_{1}+a_{2}, \ldots, a_{1}+a_{2}+\ldots+a_{n}$ all have different remainders when divided by $n+1$ ?