Let $a,$ $b,$ $c$ be positive real numbers.  Find the minimum value of
\[\frac{(a + b)(a + c)(b + c)}{abc}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a,$ $b,$ $c$ be positive real numbers.  Find the minimum value of
\[\frac{(a + b)(a + c)(b + c)}{abc}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8
Let $a,$ $b,$ $c$ be positive real numbers.  Find the minimum value of
\[\frac{(a + b)(a + c)(b + c)}{abc}.\]
train