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)

#[allow(unused_imports)]
use {
   proconio::{fastout, input, marker::*},
   std::cmp::*,
   std::collections::*,
};

#[fastout]
fn main() {
   input! {
      n: usize,
      ab: [(usize, usize); n],
      cd: [(usize, usize); n],
   }
   let mut dot = vec![((0, 0), 0); 2 * n];
   for i in 0..n {
      dot[i] = (ab[i], 0);
      dot[n + i] = (cd[i], 1);
   }
   dot.sort();

   let mut ans = 0;
   let mut red = vec![2 * n];
   for &((x, y), c) in dot.iter() {
      if c == 0 {
         red.push(y);
         red.sort();
      } else if !(red[0] > y) {
         let p = red.upper_bound(&y);
         red.remove(p - 1);
         ans += 1;
      }
   }
   println!("{}", ans);
}

/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
   fn lower_bound(&self, x: &T) -> usize;
   fn upper_bound(&self, x: &T) -> usize;
}
#[allow(dead_code)]
impl<T: Ord> BinarySearch<T> for [T] {
   fn lower_bound(&self, x: &T) -> usize {
      let mut low = 0;
      let mut high = self.len();
      while low != high {
         let mid = (low + high) / 2;
         match self[mid].cmp(x) {
            std::cmp::Ordering::Less => {
               low = mid + 1;
            }
            std::cmp::Ordering::Equal | std::cmp::Ordering::Greater => {
               high = mid;
            }
         }
      }
      low
   }
   fn upper_bound(&self, x: &T) -> usize {
      let mut low = 0;
      let mut high = self.len();
      while low != high {
         let mid = (low + high) / 2;
         match self[mid].cmp(x) {
            std::cmp::Ordering::Less | std::cmp::Ordering::Equal => {
               low = mid + 1;
            }
            std::cmp::Ordering::Greater => {
               high = mid;
            }
         }
      }
      low
   }
}