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The numbers 1,2,3,...,2017,20181,2,3,...,2017,20181,2,3,...,2017,2018 are divided into 2 groups:
a1<a2<⋯<a1009andb1>b2>⋯>b1009.a_1<a_2<\cdots<a_{1009}\qquad \text{and} \qquad b_1>b_2>\cdots>b_{1009}.a1<a2<⋯<a1009andb1>b2>⋯>b1009.
What is the sum of all possible values of ∣a1−b1∣+∣a2−b2∣+⋯+∣a1009−b1009∣?|a_1-b_1|+|a_2-b_2|+\cdots+|a_{1009}-b_{1009}|?∣a1−b1∣+∣a2−b2∣+⋯+∣a1009−b1009∣?
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