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 Scala (2.11.7) (judge verdict: Wrong Answer)

import scala.io.StdIn
object Main extends App {
  case class Point(x: Int, y: Int)
  def readPoints(n: Int): List[Point] = (0 until n).foldLeft(List.empty[Point]){
    (acc, _)  =>
      val wkp = StdIn.readLine().trim.split(' ').map(_.toInt)
      Point(wkp(0), wkp(1)) :: acc
    }
  
  def comparePoint(red: Point, blue: Point): Boolean = red.x < blue.x && red.y < blue.y
  
  val pointCount = StdIn.readLine().trim.toInt
  val redPoints = readPoints(pointCount).sortBy(e => (e.x, e.y))
  val bluePoints = readPoints(pointCount).sortBy(e => (e.x, e.y))
  
  val wk = redPoints.map{ red =>
    bluePoints.map{ blue =>
      (red, blue)
    }
  }.flatten.filter(e => comparePoint(e._1, e._2)).groupBy(e => e._1).toList.sortBy(l => (l._2.size, -l._1.x, -l._1.y))
  
  //println(wk)
  val result = wk.foldLeft(0, Set.empty[Point], Set.empty[Point]){ (acc, e) =>
    var cnt = acc._1
    var checkRed = acc._2
    var checkBlue = acc._3
    e._2.foreach{ be =>
      cnt = if(checkRed.contains(e._1) || checkBlue.contains(be._2)){
        cnt
      } else {
        checkRed += e._1
        checkBlue += be._2
        cnt + 1
      }
    }
    
    (cnt, checkRed, checkBlue)

  }

  println(result._1)
  
}