<|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
 From the sequence $1, 2, \cdots, 1982$, how can we remove the fewest numbers so that no remaining number is the product of any two other remaining numbers? Which numbers should be removed?
 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
43
From the sequence $1, 2, \cdots, 1982$, how can we remove the fewest numbers so that no remaining number is the product of any two other remaining numbers? Which numbers should be removed?

test