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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <string>
#include <algorithm>
#include <map>
#include <cmath>
#include <numeric>
using namespace std;

int main(){
    int N;
    cin >> N;
    int a[N], b[N], c[N], d[N];
    int count = 0;
    for(int i = 0; i < N; i++){
        cin >> a[i] >> b[i];
    }
    for(int i = 0; i < N; i++){
        cin >> c[i] >> d[i];   
    }
    int max_array_size = 2*N;
    int used[max_array_size][max_array_size];
    int init[max_array_size][max_array_size];
    for(int i = 0; i < max_array_size; i++){
        for(int j = 0; j < max_array_size; j++){
            init[i][j] = 0;
            used[i][j] = 0;
        }
    }
    for(int i = 0; i < N; i++){
        init[a[i]][b[i]] = 1; // red
        init[c[i]][d[i]] = 2; // blue
    }


    // look from outside
    bool is_find = false;
    for(int i = max_array_size-1; i >=0; i--){
        for(int j = max_array_size-1; j >= 0; j--){
            if(init[i][j] == 2){
                is_find = false;
                for(int l = j-1; l >= 0; l--){
                    for(int k = i-1; k >= 0; k--){
                        if(init[k][l] == 1 && used[k][l] == 0){
                            count++;
                            used[k][l] = 1;
                            is_find = true;
                            break;
                        }
                    }     
                    if(is_find == true){
                        break;
                    }
                }
            }
        }
    }
    cout << count << endl;

    return 0;
}