Maximum billboard height

You are building a billboard supported by two steel rods of equal height, one on each side. You have a collection of rods of various lengths and may weld any subset together for each side, but the two sides must end up exactly equal in total length (some rods may go unused). Return the largest possible height of the billboard (the common length), or 0 if no nonempty equal split exists. There are at most 20 rods, each length 1..1000, with total length at most 5000.