(30 marks)You are playing a game with the following strange rules as follows:There are n rooms full of identical boxes randomly distributed among these rooms. Yourgame consists of two steps:1. Chooses an arbitrary room, let's say room number i, only once.2. Move all boxes from such source room (chosen in step 1) and distribute them on the other rooms as you like.Winning/Losing Condition: If you can distribute the boxes taken from room i on the other remaining n-1 rooms in a way that makes all the remaining rooms having the same number of boxes, then you win the game, otherwise, otherwise you will lose. In order to win this strange game, I allow you to put several extra boxes into any of the existing rooms in such a way that no matter which room i you choose, you will win. What is the minimum number of extra boxes you need to put?
