<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given that 110n^3 has 110 distinct positive divisors, including 1 and 110n^3 itself, and that the prime factorization of 110 is 2 * 5 * 11, determine the number of distinct positive divisors of 81n^4. Express your answer as a single integer. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
325
Given that 110n^3 has 110 distinct positive divisors, including 1 and 110n^3 itself, and that the prime factorization of 110 is 2 * 5 * 11, determine the number of distinct positive divisors of 81n^4. Express your answer as a single integer.
test