Only approximately \(10^{605}\) cases

Algebra Level 3

The numbers \(1,2,3,...,2017,2018\) are divided into 2 groups:

\[a_1<a_2<\cdots<a_{1009}\qquad \text{and} \qquad b_1>b_2>\cdots>b_{1009}.\]

What is the sum of all possible values of \(|a_1-b_1|+|a_2-b_2|+\cdots+|a_{1009}-b_{1009}|?\)

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