US-TST 2008 Problem 1

There is a set of $n$ coins with distinct integer weights $w_1, w_2, \ldots , w_n$ . It is known that if any coin with weight $w_k$ , where $1 \leq k \leq n$ , is removed from the set, the remaining coins can be split into two groups of the same weight. (The number of coins in the two groups can be different.) Find all $n$ for which such a set of coins exists.