Let $x,$ $y,$ $z$ be positive real numbers.  Find the minimum value of
\[\frac{(1 + 5z)(4z + 3x)(5x + 6y)(y + 18)}{xyz}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x,$ $y,$ $z$ be positive real numbers.  Find the minimum value of
\[\frac{(1 + 5z)(4z + 3x)(5x + 6y)(y + 18)}{xyz}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5120
Let $x,$ $y,$ $z$ be positive real numbers.  Find the minimum value of
\[\frac{(1 + 5z)(4z + 3x)(5x + 6y)(y + 18)}{xyz}.\]
train