5. (20 points) Consider the following game. There are n players. Each player chooses a real number between 0 and 100, both ends included. The winner of the game is the person whose number is closest to 0.5a + 30, where a is the average of all players' numbers. Find all Nash equilibria of this game. If it is unique, you need to prove it. (Hint: use IESDS.)