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: Time Limit Exceeded)

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

namespace AtCoder.Beginner091
{
    public class ABC091C
    {
        public static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());

            List<Point> redPoint = new List<Point>();
            for(int i = 0; i < N; i++)
            {
                int[] nums = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                redPoint.Add(new Point() { X = nums[0], Y = nums[1] });
            }
            List<Point> bluePoint = new List<Point>();
            for(int i = 0; i < N; i++)
            {
                int[] nums = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
                bluePoint.Add(new Point() { X = nums[0], Y = nums[1] });
            }
            
            foreach(Point bp in bluePoint)
            {
                List<Point> cList;
                cList = redPoint.Where(rp => rp.X < bp.X && rp.Y < bp.Y).ToList();

                cList.Sort((a, b) => b.X - a.X);
                bp.PairCandidateXSort = new List<Point>(cList);
                
                cList.Sort((a, b) => b.Y - a.Y);
                bp.PairCandidateYSort = new List<Point>(cList);
            }
            HashSet<Point> usedPoint = new HashSet<Point>();
            int pairCnt = GetPairCount(bluePoint, 0, usedPoint);
            
            Console.WriteLine(pairCnt);
        }

        private static int GetPairCount(List<Point> bluePoint, int bi, HashSet<Point> usedPoint)
        {
            int max = usedPoint.Count;

            for(int i = bi; i < bluePoint.Count; i++)
            {
                List<Point> cList = new List<Point>();
                IEnumerable<Point> xm = bluePoint[i].PairCandidateXSort.Where((x) => !usedPoint.Contains(x));
                if(xm.Count() > 0)
                {
                    cList.Add(xm.First());
                }
                IEnumerable<Point> ym = bluePoint[i].PairCandidateYSort.Where((x) => !usedPoint.Contains(x));
                if(ym.Count() > 0)
                {
                    cList.Add(ym.First());
                }

                foreach(Point rp in cList)
                {
                    usedPoint.Add(rp);
                    int cnt;
                    if(i >= bluePoint.Count - 1)
                    {
                        cnt = usedPoint.Count;
                    }
                    else
                    {
                        cnt = GetPairCount(bluePoint, i + 1, usedPoint);
                    }
                    usedPoint.Remove(rp);
                    max = Math.Max(max, cnt);
                }
            }

            return max;
        }
    }

    public class Point
    {
        public int X;
        public int Y;
        public IEnumerable<Point> PairCandidateXSort;
        public IEnumerable<Point> PairCandidateYSort;
    }
}