AMC 12A 2002 Problem 3

According to the standard convention for exponentiation,

2^{2^{2^{2}}}=2^{\left(2^{\left(2^{2}\right)}\right)}=2^{16}=65,536 .

If the order in which the exponentiations are performed is changed, how many other values are possible?

Answer Choices
A. 0
B. 1
C. 2
D. 3
E. 4