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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

class C
{
	static void Main()
	{
		Func<int[]> read = () => Console.ReadLine().Split().Select(int.Parse).ToArray();
		var n = int.Parse(Console.ReadLine());
		var rs = new int[n].Select(_ => read()).OrderBy(p => p[0]).ToArray();
		var bs = new int[n].Select(_ => read()).OrderBy(p => p[1]).ToArray();

		var map_r = rs.Select(_ => new HashSet<int>()).ToArray();
		var map_b = bs.Select(_ => new HashSet<int>()).ToArray();
		for (int i = 0; i < n; i++)
		{
			var p = rs[i];
			for (int j = 0; j < n; j++)
			{
				var q = bs[j];
				if (p[0] < q[0] && p[1] < q[1])
				{
					map_r[i].Add(j);
					map_b[j].Add(i);
				}
			}
		}

		var c = 0;
		for (; ; c++)
		{
			var ok = false;

			for (int i = n - 1; i >= 0; i--)
			{
				if (map_r[i].Count != 1) continue;

				var j = map_r[i].First();
				foreach (var si in map_b[j])
					map_r[si].Remove(j);
				map_b[j].Clear();
				ok = true;
				break;
			}
			if (ok) continue;

			for (int j = n - 1; j >= 0; j--)
			{
				if (map_b[j].Count != 1) continue;

				var i = map_b[j].First();
				foreach (var sj in map_r[i])
					map_b[sj].Remove(i);
				map_r[i].Clear();
				ok = true;
				break;
			}
			if (ok) continue;

			for (int i = n - 1; i >= 0; i--)
			{
				if (map_r[i].Count == 0) continue;

				var j = map_r[i].Last();
				foreach (var si in map_b[j])
					map_r[si].Remove(j);
				map_b[j].Clear();
				foreach (var sj in map_r[i])
					map_b[sj].Remove(i);
				map_r[i].Clear();
				ok = true;
				break;
			}
			if (ok) continue;

			break;
		}
		Console.WriteLine(c);
	}
}