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 $|a_1-b_1|+|a_2-b_2|+\cdots+|a_{1009}-b_{1009}|?$

Only approximately 1060510^{605}10605 cases