Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\left( x + \frac{1}{y} \right) \left( x + \frac{1}{y} + 2018 \right) + \left( y + \frac{1}{x} \right) \left( y + \frac{1}{x} + 2018 \right).\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\left( x + \frac{1}{y} \right) \left( x + \frac{1}{y} + 2018 \right) + \left( y + \frac{1}{x} \right) \left( y + \frac{1}{x} + 2018 \right).\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
8080
Let $x$ and $y$ be positive real numbers.  Find the minimum value of
\[\left( x + \frac{1}{y} \right) \left( x + \frac{1}{y} + 2018 \right) + \left( y + \frac{1}{x} \right) \left( y + \frac{1}{x} + 2018 \right).\]
train