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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

# import sys
# from io import StringIO

import math

# sys.stdin = StringIO(open(__file__.replace('.py', '.in')).read())


def dist(a, b):
    if a[0] >= b[0] or a[1] >= b[1]:
        return False

    return math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2)


n = int(input())
r = []
b = []
for _ in range(n):
    r.append(list(map(int, input().split())))
for _ in range(n):
    b.append(list(map(int, input().split())))

pairs = []

for i in range(n):
    for j in range(n):
        ds = dist(r[i], b[j])
        if not ds:
            continue
        pairs.append((ds, '-'.join(map(str, r[i])), '-'.join(map(str, b[j]))))

pairs.sort(key=lambda x: x[0])

rv = set()
bv = set()

res = []

for p in pairs:
    if p[1] not in rv and p[2] not in bv:
        res.append(p)
        rv.add(p[1])
        bv.add(p[2])

# print(res)
print(len(res))