How many base-10 integers are exactly 4 digits in their base-3 representation and exactly 2 digits in their base-6 representation?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
How many base-10 integers are exactly 4 digits in their base-3 representation and exactly 2 digits in their base-6 representation?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
9
How many base-10 integers are exactly 4 digits in their base-3 representation and exactly 2 digits in their base-6 representation?
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