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 Go (1.6) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"sort"
	"strconv"
	"strings"
)

type point struct {
	x, y  int
	edges *[]*edge
}

func (a point) hasNext() bool {
	for _, edge := range *a.edges {
		if !edge.used {
			return true
		}
	}
	return false
}

type edge struct {
	used bool
	to   *point
}

type byConnectedEdge []*edge

func (a byConnectedEdge) Len() int { return len(a) }
func (a byConnectedEdge) Less(i, j int) bool {
	return len(*a[i].to.edges) < len(*a[j].to.edges)
}
func (a byConnectedEdge) Swap(i, j int) { a[i], a[j] = a[j], a[i] }

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Scan()
	l, _ := strconv.Atoi(scanner.Text())

	sPoint := &point{-1, -1, &[]*edge{}}
	tPoint := &point{-2, -2, &[]*edge{}}

	redPoints := []*point{}
	idx := 0
	for scanner.Scan() {
		pointArray := strings.Split(scanner.Text(), " ")
		x, _ := strconv.Atoi(pointArray[0])
		y, _ := strconv.Atoi(pointArray[1])
		if idx < l {
			r := point{x, y, &[]*edge{}}
			*sPoint.edges = append(*(sPoint.edges), &edge{false, &r})
			redPoints = append(redPoints, &r)
		} else {
			b := &point{x, y, &[]*edge{&edge{false, tPoint}}}
			for _, r := range redPoints {
				if r.x < x && r.y < y {
					*r.edges = append(*r.edges, &edge{false, b})
				}
			}
		}
		idx++
	}

	sort.Sort(byConnectedEdge(*sPoint.edges))

	cnt := 0
	for _, sNext := range *sPoint.edges {
		if sNext.used {
			continue
		}
		if findPathToT(sNext.to) {
			cnt++
		}
	}

	fmt.Println(cnt)
}

func findPathToT(current *point) bool {
	if current.x == -2 && current.y == -2 {
		return true
	}

	if !current.hasNext() {
		return false
	}

	for _, next := range *current.edges {
		if next.used {
			continue
		}
		next.used = true
		arrived := findPathToT(next.to)
		if arrived {
			//残余
			*next.to.edges = append(*next.to.edges, &edge{false, current})
			return true
		}
		next.used = false
	}
	return false
}