NMC 1989 Problem 4

For which positive integers $n$ is the following statement true: if $a_1, a_2, ... , a_n$ are positive integers, $a_k \le n$ for all $k$ and $\sum\limits_{k=1}^{{n}}{a_k}=2n$ then it is always possible to choose $a_{i1} , a_{i2} , ..., a_{ij}$ in such a way that the indices $i_1, i_2,... , i_j$ are different numbers, and $\sum\limits_{k=1}^{{{j}}}{a_{ik}}=n$ ?