Suppose you are given a set S of n integers. You are also given a black box that returns three elements a,b, c ?S such that a + b + c = 0 if any such elements exist. Devise an algorithm that uses only one call to the black box to determine if S contains any three integers a,b,c such that a + b = c. (Hint: Construct a set S' so that the following holds: there exist a', b', c'? S' such that a' + b' + c' = 0 if and only if there exist a, b, c ? S such that a + b = c.)