Problem:
Score : 400 points

Problem Statement

On a two-dimensional plane, there are N red points and N blue points.
The coordinates of the i-th red point are (a_i, b_i), and the coordinates of the i-th blue point are (c_i, d_i).

A red point and a blue point can form a friendly pair when, the x-coordinate of the red point is smaller than that of the blue point, and the y-coordinate of the red point is also smaller than that of the blue point.

At most how many friendly pairs can you form? Note that a point cannot belong to multiple pairs.

Constraints

All input values are integers.

1 \leq N \leq 100

0 \leq a_i, b_i, c_i, d_i < 2N

a_1, a_2, ..., a_N, c_1, c_2, ..., c_N are all different.

b_1, b_2, ..., b_N, d_1, d_2, ..., d_N are all different.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
a_2 b_2
:
a_N b_N
c_1 d_1
c_2 d_2
:
c_N d_N

Output

Print the maximum number of friendly pairs.

Sample Input 1

3
2 0
3 1
1 3
4 2
0 4
5 5

Sample Output 1

2

For example, you can pair (2, 0) and (4, 2), then (3, 1) and (5, 5).

Sample Input 2

3
0 0
1 1
5 2
2 3
3 4
4 5

Sample Output 2

2

For example, you can pair (0, 0) and (2, 3), then (1, 1) and (3, 4).

Sample Input 3

2
2 2
3 3
0 0
1 1

Sample Output 3

0

It is possible that no pair can be formed.

Sample Input 4

5
0 0
7 3
2 2
4 8
1 6
8 5
6 9
5 4
9 1
3 7

Sample Output 4

5

Sample Input 5

5
0 0
1 1
5 5
6 6
7 7
2 2
3 3
4 4
8 8
9 9

Sample Output 5

4

Solution in Rust (1.42.0) (judge verdict: Accepted)

use std::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

#[derive(Clone)]
struct Edge<T: Clone> {
    to: usize,
    cap: T,
    rev: usize,
}

pub struct Graph<T: Clone> {
    edges: Vec<Vec<Edge<T>>>,
}

impl<T: Clone> Graph<T> {
    pub fn new(n: usize) -> Self {
        Graph {
            edges: vec![Vec::new(); n],
        }
    }
}

impl Graph<i64> {

    pub fn add_edge(&mut self, from: usize, to: usize, cap: i64) {
        let flen = self.edges[from].len();
        let tlen = self.edges[to].len();
        self.edges[from].push(Edge { to, cap, rev: tlen });
        self.edges[to].push(Edge { to: from, cap: 0, rev: flen });
    }

    fn dfs(&mut self, v: usize, t: usize, f: i64, used: &mut Vec<bool>) -> i64 {
        if v == t {
            return f;
        }
        used[v] = true;
        for i in 0..self.edges[v].len() {
            let eto = self.edges[v][i].to;
            let ecap = self.edges[v][i].cap;
            let erev = self.edges[v][i].rev;
            if !used[eto] && ecap > 0 {
                let d = self.dfs(eto, t, std::cmp::min(f, ecap), used);
                if d > 0 {
                    self.edges[v][i].cap -= d;
                    self.edges[eto][erev].cap += d;
                    return d;
                }
            }
        }
        0
    }

    pub fn max_flow(&mut self, s: usize, t: usize, inf: i64) -> i64 {
        let mut flow = 0;
        let mut used = vec![false; self.edges.len()];
        loop {
            used.iter_mut().for_each(|x| *x = false);
            let f = self.dfs(s, t, inf, &mut used);
            if f == 0 {
                return flow;
            }
            flow += f;
        }
    }
}

fn main() {
    let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = line[0];
    let mut red = Vec::with_capacity(n);
    let mut blue = Vec::with_capacity(n);
    for i in 0..n {
        let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let a = line[0];
        let b = line[1];
        red.push((a, b));
    }
    for i in 0..n {
        let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
        let c = line[0];
        let d = line[1];
        blue.push((c, d));
    }
    let mut graph = Graph::new(2*n + 2);
    for i in 0..n {
        for j in 0..n {
            if red[i].0 < blue[j].0 && red[i].1 < blue[j].1 {
                graph.add_edge(i, j+n, 1);
            }
        }
    }
    for i in 0..n {
        graph.add_edge(2*n, i, 1);
        graph.add_edge(n + i, 2*n + 1, 1);
    }

    println!("{}", graph.max_flow(2*n, 2*n+1, 1_000_000));
}