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: Wrong Answer)

fn main() {
    proconio::input! {
        n: usize,
        abs: [(usize, usize); n], // red
        cds: [(usize, usize); n], // blue
    }
    let mut ok_cds_of_abs = std::collections::HashMap::<
        (usize, usize),
        std::collections::HashSet<(usize, usize)>,
    >::new();
    let mut ok_abs_of_cds = std::collections::HashMap::<
        (usize, usize),
        std::collections::HashSet<(usize, usize)>,
    >::new();
    for (a, b) in &abs {
        for (c, d) in &cds {
            if a < c && b < d {
                ok_cds_of_abs
                    .entry((*a, *b))
                    .or_insert(std::collections::HashSet::new())
                    .insert((*c, *d));
                ok_abs_of_cds
                    .entry((*c, *d))
                    .or_insert(std::collections::HashSet::new())
                    .insert((*a, *b));
            }
        }
    }
    let mut count = 0usize;
    while !ok_cds_of_abs.is_empty() {
        let min_ab = *ok_cds_of_abs
            .iter()
            .min_by(|l, r| l.1.len().cmp(&r.1.len()))
            .unwrap()
            .0;
        let min_cd = *ok_abs_of_cds
            .iter()
            .min_by(|l, r| l.1.len().cmp(&r.1.len()))
            .unwrap()
            .0;
        count += 1;
        if ok_cds_of_abs.get(&min_ab).unwrap().len() <= ok_abs_of_cds.get(&min_cd).unwrap().len() {
            let cd = *ok_cds_of_abs.get(&min_ab).unwrap().iter().next().unwrap();
            ok_cds_of_abs.remove(&min_ab);
            ok_abs_of_cds.iter_mut().for_each(|(_cd, abs)| {
                abs.remove(&min_ab);
            });
            ok_abs_of_cds.remove(&cd);
            ok_cds_of_abs.iter_mut().for_each(|(_ab, cds)| {
                cds.remove(&cd);
            });
        } else {
            let ab = *ok_abs_of_cds.get(&min_cd).unwrap().iter().next().unwrap();
            ok_abs_of_cds.remove(&min_cd);
            ok_cds_of_abs.iter_mut().for_each(|(_ab, cds)| {
                cds.remove(&min_cd);
            });
            ok_cds_of_abs.remove(&ab);
            ok_abs_of_cds.iter_mut().for_each(|(_cd, abs)| {
                abs.remove(&ab);
            });
        }
        let v = ok_cds_of_abs
            .iter()
            .filter(|(_key, value)| value.is_empty())
            .map(|(k, _)| *k)
            .collect::<Vec<(usize, usize)>>();
        for item in v {
            ok_cds_of_abs.remove(&item);
        }
        let v = ok_abs_of_cds
            .iter()
            .filter(|(_key, value)| value.is_empty())
            .map(|(k, _)| *k)
            .collect::<Vec<(usize, usize)>>();
        for item in v {
            ok_abs_of_cds.remove(&item);
        }
    }
    println!("{}", count);
}