Find the product of $123_4 \cdot 3_4$.  Express your answer in base 4.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the product of $123_4 \cdot 3_4$.  Express your answer in base 4.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1101_4
Find the product of $123_4 \cdot 3_4$.  Express your answer in base 4.
train