For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1000
For how many positive integers $m,$ $1 \le m \le 1000,$ does there exist at least one positive integer $n$ such that $m \cdot n \le m + n$?
train