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: Wrong Answer)

package main

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

type point struct {
	x, y int
}

type pairCandidates struct {
	red           point
	blueCandidate map[point]bool
}

type byNumberOfCandidate []pairCandidates

func (a byNumberOfCandidate) Len() int {
	return len(a)
}

func (a byNumberOfCandidate) Less(i, j int) bool {
	return len(a[i].blueCandidate) < len(a[j].blueCandidate)
}

func (a byNumberOfCandidate) 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())

	redPoints := []point{}
	bluePoints := []point{}
	idx := 0
	for scanner.Scan() {
		pointArray := strings.Split(scanner.Text(), " ")
		x, _ := strconv.Atoi(pointArray[0])
		y, _ := strconv.Atoi(pointArray[1])
		if idx < l {
			redPoints = append(redPoints, point{x, y})
		} else {
			bluePoints = append(bluePoints, point{x, y})
		}
		idx++
	}

	blueCandidatesForRed := []pairCandidates{}
	for _, r := range redPoints {
		blueCandidates := map[point]bool{}
		for _, b := range bluePoints {
			if r.x < b.x && r.y < b.y {
				blueCandidates[b] = true
			}
		}
		blueCandidatesForRed = append(blueCandidatesForRed, pairCandidates{r, blueCandidates})
	}

	//sort
	sort.Sort(byNumberOfCandidate(blueCandidatesForRed))

	//reduce
	pairCnt := 0
	for {
		if len(blueCandidatesForRed) == 0 {
			break
		}

		pairCandidate := blueCandidatesForRed[0]
		blueCandidates := pairCandidate.blueCandidate
		if len(blueCandidates) == 0 {
			blueCandidatesForRed = blueCandidatesForRed[1:]
			continue
		}
		var fixedBlue point
		for p := range blueCandidates {
			fixedBlue = p
			break
		}
		pairCnt++
		blueCandidatesForRed = blueCandidatesForRed[1:]
		//remove fixedBlue from blueCandidates
		for _, nextPairCandidate := range blueCandidatesForRed {
			delete(nextPairCandidate.blueCandidate, fixedBlue)
		}

		sort.Sort(byNumberOfCandidate(blueCandidatesForRed))
	}
	fmt.Println(pairCnt)
}