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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

bool comparePair(pair<int, int> a, pair<int, int> b) {
  if(a.first!= b.first) return a.first < b.first;
  else return a.second < b.second;
}

int main() {
  int N; cin >> N;
  vector<pair<int, int>> red(N);
  vector<pair<int, int>> blue(N);
  for (int i=0; i<N; i++) cin >> red[i].first >> red[i].second;
  for (int i=0; i<N; i++) cin >> blue[i].first >> blue[i].second;
  sort(red.begin(), red.end(), comparePair);
  sort(blue.begin(), blue.end(), comparePair);
  double grad, mingrad;
  int mingradidx, ans=0;
  for (int i=0; i<N; i++) {
    grad=0;mingrad=200;mingradidx=0;
    for (int j=0; j<N; j++) {
      if (blue[j].first>red[i].first&&blue[j].second>red[i].second) {
        grad=(blue[j].second-red[i].second) / (blue[j].first-red[i].first);
        if (grad < mingrad) {mingrad = grad; mingradidx=j;}
      }
    }
    if(grad>0) {ans++; blue[mingradidx].first=0; blue[mingradidx].second=0;}
  }
  cout << ans << "\n";
}