There are $2n$ distinct points on a circle. The numbers $1$ through $2n$ are randomly assigned to this one points distributed. Each point is connected to exactly one other point, so that no of the resulting connecting routes intersect. If a segment connects the numbers $a$ and $b$, so we assign the value $ |a - b|$ to the segment . Show that we can choose the routes such that the sum of these values results $n^2$.