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 (1.15.1) (judge verdict: Time Limit Exceeded)

#[allow(unused_imports)]
use std::io::*;
#[allow(unused_imports)]
use std::str::*;
#[allow(unused_imports)]
use std::mem::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::HashMap;
#[allow(unused_imports)]
use std::collections::VecDeque;
#[allow(unused_imports)]
use std::usize;

#[allow(unused_macros)]
macro_rules! read_cols {
    ($($t:ty),+) => {{
        let mut line = String::new();
        stdin().read_line(&mut line).unwrap();

        let mut it = line.trim()
            .split_whitespace();

        ($(
            it.next().unwrap().parse::<$t>().ok().unwrap()
        ),+)
    }}
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();
    line.trim().to_string().parse().ok().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: FromStr>() -> Vec<T> {
    let mut line = String::new();
    stdin().read_line(&mut line).unwrap();

    line.trim()
        .split_whitespace()
        .map(|s| s.parse().ok().unwrap())
        .collect()
}

fn execute(red: &[(usize, usize)], blue: &Vec<(usize, usize)>, used_blue: &mut Vec<bool>) -> usize {
    let mut ans = 0;

    let (&r, remains) = match red.split_first() {
        Some(r) => r,
        None => return 0,
    };

    let if_none = execute(remains, blue, used_blue);

    let mut candidates: Vec<(usize, (usize, usize))> = blue.iter()
        .enumerate()
        .skip_while(|&(_, &(x, _))| x < r.0)
        .filter(|&(i, _)| !used_blue[i])
        .map(|(i, &p)| (i, p))
        .collect();
    // 上から下
    candidates.sort_by(|&(_, (x1, y1)), &(_, (x2, y2))| y1.cmp(&y2));
    let candidate = candidates.first();
    match candidate {
        Some(&(i, _)) => {
            used_blue[i] = true;
            let if_take = execute(remains, blue, used_blue);
            used_blue[i] = false;
            max(if_take + 1, if_none)
        }
        None => if_none
    }
}

fn main() {
    let n = read::<usize>();
    let mut red = Vec::new();
    for _ in 0..n {
        let (a, b) = read_cols!(usize, usize);
        red.push((a, b));
    }
    let mut blue = Vec::new();
    for _ in 0..n {
        let (a, b) = read_cols!(usize, usize);
        blue.push((a, b));
    }

    // 右から左
    red.sort_by(|&(x1, y1), &(x2, y2)| x2.cmp(&x1));
    // 左から右
    blue.sort_by(|&(x1, y1), &(x2, y2)| x1.cmp(&x2));

    let mut used_blue = Vec::new();
    used_blue.resize(n, false);

    println!("{}", execute(&red, &blue, &mut used_blue));
}