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# (.NET Core 3.1.201) (judge verdict: Accepted)

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 r = new int[n].Select(_ => Read()).ToArray();
		var b = new int[n].Select(_ => Read()).ToArray();

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

		Console.WriteLine(MaxFlow(ev, sv, ev, 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 e in dag)
		{
			map[e[0]].Add(new[] { e[1], e[2], map[e[1]].Count });
			map[e[1]].Add(new[] { e[0], 0, map[e[0]].Count - 1 });
		}

		long Bfs()
		{
			var from = new long[n + 1][];
			var u = new bool[n + 1];
			var minFlow = Enumerable.Repeat(long.MaxValue, n + 1).ToArray();
			var q = new Queue<long>();
			q.Enqueue(sv);

			while (q.TryDequeue(out var v))
			{
				if (v == ev) break;
				foreach (var e in map[v])
				{
					if (u[e[0]] || e[1] == 0) continue;
					from[e[0]] = e;
					u[e[0]] = true;
					minFlow[e[0]] = Math.Min(minFlow[v], e[1]);
					q.Enqueue(e[0]);
				}
			}

			if (from[ev] == null) return 0;
			long tv = ev;
			while (true)
			{
				from[tv][1] -= minFlow[ev];
				var rev = map[from[tv][0]][(int)from[tv][2]];
				rev[1] += minFlow[ev];
				if ((tv = rev[0]) == sv) break;
			}
			return minFlow[ev];
		}

		long M = 0, t;
		while ((t = Bfs()) > 0) M += t;
		return M;
	}
}