<|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
 Find the natural number \( n \) that is the product of the primes \( p, q, \) and \( r \), given that

\[ 
r - q = 2p \quad \text{and} \quad rq + p^2 = 676 
\] 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
2001
Find the natural number \( n \) that is the product of the primes \( p, q, \) and \( r \), given that

\[ 
r - q = 2p \quad \text{and} \quad rq + p^2 = 676 
\]
test