What is the greatest positive integer $n$ such that $3^n$ is a factor of $200!$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
What is the greatest positive integer $n$ such that $3^n$ is a factor of $200!$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
97
What is the greatest positive integer $n$ such that $3^n$ is a factor of $200!$?
train