Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard.Bob appends another digit from the set M until a 2n-digit number is reached, where n is a positive integer.If this number is divisible by 9, Bob wins, otherwise Alice wins.For which n can Alice win and for which n can Bob win?