Find the remainder when $3^{1999}$ is divided by $13$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the remainder when $3^{1999}$ is divided by $13$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
Find the remainder when $3^{1999}$ is divided by $13$.
train