409101: GYM103438 G Max Pair Matching

You are given $$$2n$$$ pairs $$$(a_i, b_i)$$$ of integers. Consider a complete graph on $$$2n$$$ vertices and define the weight of the edge $$$(ij)$$$ to be $$$w_{ij} = max(|a_i-a_j|, |a_i-b_j|, |b_i-a_j|, |b_i-b_j|)$$$.

Determine the maximum weight of the matching in this graph.

In other words, consider all ways to select $$$n$$$ edges of this graph such that no two chosen edges have a common endpoint. What is the maximum possible total weight of these edges?

The first line of the input contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$).

The $$$i$$$-th of the next $$$2n$$$ lines contain two integers $$$a_i$$$ and $$$b_i$$$ ($$$0 \le a_i, b_i \le 10^9$$$).

Print a single integer — the maximum weight of the matching in this graph.

2
0 10
7 7
9 4
2 15

18

Adjacency matrix: