Problem: 351E - Jeff and Permutation

Abridged statement: given n ≤ 2000 integers, we can multiply some of them by  - 1. Goal is to minimize number of inversions (pairs (i, j) such that i < j and a_i > a_j). Print the minimum number of inversions.

Solution: 30244905

This solution replaces all numbers with its absolute value first. Then for each index i this solution adds min(L, R) to answer where L =  number of smaller elements to left, R =  number of smaller elements to right. Why does it work?