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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

struct point{
    int x;
    int y;
    int already;
};

void select_sort(struct point poi[200], int N){
    for(int i = 0; i < N; i++){
        int min_index = i;
        int min_x = poi[i].x;
        int min_y = poi[i].y;
        
        for(int j = i + 1; j < N; j++){
            if(min_x > poi[j].x && min_y > poi[j].y){
                min_x = poi[j].x;
                min_y = poi[j].y;
                min_index = j;
            }
        }
        if (min_index != i){
            poi[i].x += poi[min_index].x;
            poi[min_index].x = poi[i].x - poi[min_index].x;
            poi[i].x -= poi[min_index].x;
            
            poi[i].y += poi[min_index].y;
            poi[min_index].y = poi[i].y - poi[min_index].y;
            poi[i].y -= poi[min_index].y;
            
            
        }
    }
}

int main(int argc, const char * argv[]) {
    
    int N = 0;
    scanf("%d", &N);
    
    struct point red[200];
    struct point blue[200];
    
    for(int i = 0; i < N; i++){
        scanf("%d%d", &red[i].x, &red[i].y);
        red[i].already = 0;
    }
    for(int i = 0; i < N; i++){
        scanf("%d%d", &blue[i].x, &blue[i].y);
        blue[i].already = 0;
    }
    select_sort(red, N);
    select_sort(blue, N);
    
    int count = 0;
    for(int i = 0; i < N; i++){
        int index = 0;
        double min = 10000000;
        for(int j = 0; j < N; j++){
            if(red[j].x > blue[i].x && red[j].y > blue[i].y){
                if(min == 10000000)
                    break;
                red[index].already = 1;
                count++;
                min = 10000000;
                break;
            }
            
            if(red[j].x < blue[i].x && red[j].y < blue[i].y && red[j].already == 0){
                if(min > sqrt(pow(red[j].x - blue[i].x,2) + pow(red[j].y - blue[i].y,2))){
                    min = sqrt(pow(red[j].x - blue[i].x,2) + pow(red[j].y - blue[i].y,2));
                    index = j;
                }
            }
        }
        
        if(min != 10000000){
            red[index].already = 1;
            count++;
        }
    }
    printf("%d\n", count);
    return 0;
}