The first 2n positive integers are arbitrarily divided into two groups of n numbers each. The numbers in the first group are sorted in ascending order:a1 < a2 < ... < an; the numbers in the second group are sorted in descending order: b1 > b2 > ... > bn.
Find, with proof, the value of the sum |a1 − b1| + |a2 − b2| + ... + |an − bn|.