USA math olympiad problem

Show that for any fixed integer n >=1, the sequence: 2, 2^2, 2^(2^2), 2^(2^(2^2))... mod n $$
is eventually constant. [That is, the sequence is defined: a_1=2, ai+1 = 2a_i. and you need to show that, for any positive integer n, the sequence a_1 mod n, a_2 mod n, .... is eventually constant.]