# Only approximately $10^{605}$ cases

Algebra Level 3

The numbers $1,2,3,...,2017,2018$ are divided into 2 groups:

$a_1b_2>\cdots>b_{1009}.$

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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