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 <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <cstring>
#include <queue>
#include <map>
#define pb push_back
using namespace std;
typedef pair<int,int> pii;
typedef long long int lli;


struct mypair{
  int x,y;
  mypair(int a,int b){ x=a; y=b;}
  bool operator<( const mypair& another) const {
    //if(x==another.x) return y < another.y;
    //return min(x,y) < min(another.x,another.y);
    return x*x + y*y < another.x* another.x + another.y*another.y;
  }
};


int n;
vector<mypair> aka,ao;
bool use[111];

int main(void){
  cin>>n;
  int a,b,c,d;
  for(int i=1;i<=n;i++){
    cin>>a>>b;
    aka.pb(mypair(a,b));
  }
  for(int i=1;i<=n;i++){
    cin>>c>>d;
    ao.pb(mypair(c,d));
  }
  sort(aka.begin(),aka.end());
  sort(ao.begin(),ao.end());
  
  int tmp1,tmp2;
  tmp1=tmp2=0;
  
  for(int i=0;i<n;i++){
    //printf("%d %d %d %d\n",aka[i].x,aka[i].y,ao[i].x,ao[i].y);
  }
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      if(use[j]) continue;
      if(aka[i].x<ao[j].x && aka[i].y<ao[j].y){
	tmp1++;
	use[j]=true;
	break;
      }
    }
  }
  for(int i=0;i<=111;i++) use[i]=false;
  for(int j=0;j<n;j++){
    for(int i=0;i<n;i++){
      if(use[j]) continue;
      if(aka[i].x<ao[j].x && aka[i].y<ao[j].y){
	tmp2++;
	use[i]=true;
	break;
      }
    }
  }
  cout<<max(tmp1,tmp2)<<endl;
  return 0;
}