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)

n = int(input())

red = []
blue = []
ed = []
for i in range(n):
    red.append(list(map(int,input().split())))
for i in range(n):
    blue.append(list(map(int,input().split())))

inf = 10**30

node = n*2+2

for i in range(1,n+1):
    ed.append([0,i,1])
    ed.append([n+i,2*n+1,1])
    
for i in range(n):
    for j in range(n):
        if red[i][0]<blue[j][0] and red[i][1]<blue[j][1]:
            ed.append([i+1,j+n+1,1])
    


edge = len(ed)
start = 0
goal = 2*n+1

"""
limit = [[0 for i in range(node)] for j in range(node)]
for i in edge:
    limit[i[0]][i[1]] += i[2]
"""

limit = [[] for i in range(node)]
for i in ed:
    limit[i[0]].append([i[1],i[2]])
    limit[i[1]].append([i[0],0])

ans = 0
while True:
    used = [False for i in range(node)]
    used[start] = True
    stack = [start]
    pre = [False for i in range(node)] # posの前
    pcos = [inf for i in range(node)] # posまでのコスト
    flg = False
    while stack:
        # print(stack)
        pos = stack.pop()
        for e in limit[pos]:
            if e[1] != 0 and (not used[e[0]]):
                pre[e[0]]=pos
                pcos[e[0]]=e[1]
                stack.append(e[0])
                used[e[0]]=True
                if e[0]==goal:
                    stack = []
                    flg = True
    if flg==False:
        print(ans)
        break
    pos = goal
    root = []
    minicost = inf
    while pos != start:
        root.append(pos)
        minicost = min(minicost,pcos[pos])
        pos = pre[pos]
    root.append(start)
    root.reverse()
    ans += minicost
    for i in range(len(root)-1):
        for j in range(len(limit[root[i]])):
            if limit[root[i]][j][0]==root[i+1]:
                limit[root[i]][j] = [root[i+1],limit[root[i]][j][1]-minicost]
        for j in range(len(limit[root[i+1]])):
            if limit[root[i+1]][j][0] == root[i]:
                limit[root[i+1]][j] = [root[i],limit[root[i+1]][j][1]+minicost]