According to the standard convention for exponentiation,  
$$2^{2^{2^{2}}} = 2^{(2^{(2^2)})} = 2^{16} = 65536.$$   
If the order in which the exponentiations are performed is changed, how many other values are possible? Provide your answer as an integer.

Let's think step by step and output the final answer within \boxed{}.
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