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-csc 3.5.0) (judge verdict: Time Limit Exceeded)

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

class C
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var rs = new int[n].Select(_ => Read()).ToArray();
		var bs = new int[n].Select(_ => Read()).ToArray();

		var dag = new List<long[]>();
		dag.AddRange(Enumerable.Range(1, n).Select(i => new[] { 0, i, 1L }));
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				if (rs[i][0] < bs[j][0] && rs[i][1] < bs[j][1])
					dag.Add(new[] { i + 1, n + j + 1, 1L });
		dag.AddRange(Enumerable.Range(n + 1, n).Select(i => new[] { i, 2 * n + 1, 1L }));

		Console.WriteLine(MaxFlow(2 * n + 1, 0, 2 * n + 1, dag.ToArray()));
	}

	static long MaxFlow(int n, int sv, int ev, long[][] dag)
	{
		var map = Array.ConvertAll(new int[n + 1], _ => new List<long[]>());
		foreach (var r in dag)
		{
			map[r[0]].Add(new[] { r[1], r[2], map[r[1]].Count });
			map[r[1]].Add(new[] { r[0], 0, map[r[0]].Count - 1 });
		}

		var u = new bool[n + 1];
		long Dfs(long v, long min)
		{
			if (v == ev) return min;
			u[v] = true;
			foreach (var r in map[v])
			{
				if (u[r[0]] || r[1] == 0) continue;
				var delta = Dfs(r[0], Math.Min(min, r[1]));
				if (delta > 0)
				{
					r[1] -= delta;
					map[r[0]][(int)r[2]][1] += delta;
					u[v] = false;
					return delta;
				}
			}
			u[v] = false;
			return 0;
		}

		long M = 0, t;
		while ((t = Dfs(sv, long.MaxValue)) > 0) M += t;
		return M;
	}
}