<|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
 A flea jumps along the number line, where the length of each jump cannot be less than $n$. It starts its movement from the origin and wants to visit all integer points on the segment $[0, 2013]$ (and only them!) exactly once. For what maximum value of $n$ can it achieve this? 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
1006
A flea jumps along the number line, where the length of each jump cannot be less than $n$. It starts its movement from the origin and wants to visit all integer points on the segment $[0, 2013]$ (and only them!) exactly once. For what maximum value of $n$ can it achieve this?
test