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 Python (3.4.3) (judge verdict: Accepted)

from collections import namedtuple

N = int(input())
ab = [tuple(map(int, input().split())) for i in range(N)]
cd = [tuple(map(int, input().split())) for i in range(N)]

G = [[] for i in range(N * 2 + 2)]

Edge = namedtuple("Edge", ("to", "cap", "rev"))

def add_edge(frm, to, cap):
    G[frm].append(Edge(to, cap, len(G[to])))
    G[to].append(Edge(frm, 0, len(G[frm]) - 1))

# 現在の頂点, 終点, 増加フロー
def dfs(v, t, f):
    if v == t:
        return f
    used[v] = True
    for i, e in enumerate(G[v]):
        if not used[e.to] and e.cap > 0:
            d = dfs(e.to, t, min(f, e.cap))
            if d > 0:
                G[v][i] = Edge(e.to, e.cap - d, e.rev)
                G[e.to][e.rev] = Edge(v, G[e.to][e.rev].cap + d, i)
                return d
    return 0

for i in range(1, N + 1):
    add_edge(0, i, 1)
    add_edge(N + i, N * 2 + 1, 1)

for i in range(1, N + 1):
    a, b = ab[i - 1]
    for j in range(1, N + 1):
        c, d = cd[j - 1]
        if a < c and b < d:
            add_edge(i, N + j, 1)            

flow = 0
while 1:
    used = [False for i in range(N * 2 + 2)]
    f = dfs(0, N * 2 + 1, 114514)
    if f == 0:
        break
    flow += f

print(flow)