#include<bits/stdc++.h>
using namespace std;
#define ms(x,y) memset(x,y,sizeof(x))
struct node
{
	int x,y;
}a[102];
node b[102];
int vis[102],cx[102],cy[102],e[102][102];
int n;
int dfs(int x)
{
	for(int y= 1;y<=n;y++)
	{
		if(e[x][y] && !vis[y])
		{
			vis[y] = 1;
			if(cy[y] == -1 || dfs(cy[y]) )
			{
				cx[x] = y;
				cy[y] = x;
				return 1;
			}
		}
	}
	return 0;
}
int main()
{
	ms(e,0);ms(cx,-1);ms(cy,-1);
	
	cin>>n;
	for(int i= 1;i<=n;i++)
	{
		cin>>a[i].x>>a[i].y;
	}
	for(int i = 1;i<=n;i++)
	{
		cin>>b[i].x>>b[i].y;
	}
	int ans = 0;
	for(int i = 1;i<=n;i++)
	{
		for(int j = 1;j<=n;j++)
		{
			if(a[i].x < b[j].x && a[i].y<b[j].y)
			{
				e[i][j] = 1;
			}
		}
	}
	for(int i = 1;i<=n;i++)
	{
		ms(vis,0);
		ans += dfs(i);
	}
	cout<<ans <<endl;
	return 0;
}
### Prompt

Please create a solution in Cpp to the following problem:

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.

Examples

Input

3
2 0
3 1
1 3
4 2
0 4
5 5


Output

2


Input

3
0 0
1 1
5 2
2 3
3 4
4 5


Output

2


Input

2
2 2
3 3
0 0
1 1


Output

0


Input

5
0 0
7 3
2 2
4 8
1 6
8 5
6 9
5 4
9 1
3 7


Output

5


Input

5
0 0
1 1
5 5
6 6
7 7
2 2
3 3
4 4
8 8
9 9


Output

4

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
#define ms(x,y) memset(x,y,sizeof(x))
struct node
{
	int x,y;
}a[102];
node b[102];
int vis[102],cx[102],cy[102],e[102][102];
int n;
int dfs(int x)
{
	for(int y= 1;y<=n;y++)
	{
		if(e[x][y] && !vis[y])
		{
			vis[y] = 1;
			if(cy[y] == -1 || dfs(cy[y]) )
			{
				cx[x] = y;
				cy[y] = x;
				return 1;
			}
		}
	}
	return 0;
}
int main()
{
	ms(e,0);ms(cx,-1);ms(cy,-1);
	
	cin>>n;
	for(int i= 1;i<=n;i++)
	{
		cin>>a[i].x>>a[i].y;
	}
	for(int i = 1;i<=n;i++)
	{
		cin>>b[i].x>>b[i].y;
	}
	int ans = 0;
	for(int i = 1;i<=n;i++)
	{
		for(int j = 1;j<=n;j++)
		{
			if(a[i].x < b[j].x && a[i].y<b[j].y)
			{
				e[i][j] = 1;
			}
		}
	}
	for(int i = 1;i<=n;i++)
	{
		ms(vis,0);
		ans += dfs(i);
	}
	cout<<ans <<endl;
	return 0;
}
```