Find the sum of the squares of the solutions to
\[\left| x^2 - x + \frac{1}{2008} \right| = \frac{1}{2008}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the sum of the squares of the solutions to
\[\left| x^2 - x + \frac{1}{2008} \right| = \frac{1}{2008}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{1003}{502}
Find the sum of the squares of the solutions to
\[\left| x^2 - x + \frac{1}{2008} \right| = \frac{1}{2008}.\]
train