39. It is known that , , and will enter an election in that order, with announcing his position first, then , and finally . If the distribution is uniform (rectangular) over [0, 1], what position should each candidate take to maximize his or her vote total, anticipating—in the case of and —the entry of future candidates? [Hint: Start by assuming that takes a position at . Is 's position at optimal, anticipating the entry of ? Or can do better at some other position (perhaps by influencing 's choice of a maximizing position)?]