Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

brute force

combinatorics

constructive algorithms

dfs and similar

graph matchings

greedy

math

*2600

No tag edit access

The problem statement has recently been changed. View the changes.

×
E. Sum of Matchings

time limit per test

4 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputLet's denote the size of the maximum matching in a graph $$$G$$$ as $$$\mathit{MM}(G)$$$.

You are given a bipartite graph. The vertices of the first part are numbered from $$$1$$$ to $$$n$$$, the vertices of the second part are numbered from $$$n+1$$$ to $$$2n$$$. Each vertex's degree is $$$2$$$.

For a tuple of four integers $$$(l, r, L, R)$$$, where $$$1 \le l \le r \le n$$$ and $$$n+1 \le L \le R \le 2n$$$, let's define $$$G'(l, r, L, R)$$$ as the graph which consists of all vertices of the given graph that are included in the segment $$$[l, r]$$$ or in the segment $$$[L, R]$$$, and all edges of the given graph such that each of their endpoints belongs to one of these segments. In other words, to obtain $$$G'(l, r, L, R)$$$ from the original graph, you have to remove all vertices $$$i$$$ such that $$$i \notin [l, r]$$$ and $$$i \notin [L, R]$$$, and all edges incident to these vertices.

Calculate the sum of $$$\mathit{MM}(G(l, r, L, R))$$$ over all tuples of integers $$$(l, r, L, R)$$$ having $$$1 \le l \le r \le n$$$ and $$$n+1 \le L \le R \le 2n$$$.

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 1500$$$) — the number of vertices in each part.

Then $$$2n$$$ lines follow, each denoting an edge of the graph. The $$$i$$$-th line contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i \le n$$$; $$$n + 1 \le y_i \le 2n$$$) — the endpoints of the $$$i$$$-th edge.

There are no multiple edges in the given graph, and each vertex has exactly two incident edges.

Output

Print one integer — the sum of $$$\mathit{MM}(G(l, r, L, R))$$$ over all tuples of integers $$$(l, r, L, R)$$$ having $$$1 \le l \le r \le n$$$ and $$$n+1 \le L \le R \le 2n$$$.

Example

Input

5 4 6 4 9 2 6 3 9 1 8 5 10 2 7 3 7 1 10 5 8

Output

314

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/14/2024 04:37:09 (j2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|