C - 2D Plane 2N Points

Time Limit: 2 sec / Memory Limit: 256 MB

問題文

あなたは最大で何個の仲良しペアを作ることができますか？ ただし，1 つの点が複数のペアに所属することはできません。

制約

• 入力は全て整数
• 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 はすべて異なる
• b_1, b_2, ..., b_N, d_1, d_2, ..., d_N はすべて異なる

入力

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


入力例 1

3
2 0
3 1
1 3
4 2
0 4
5 5


出力例 1

2


入力例 2

3
0 0
1 1
5 2
2 3
3 4
4 5


出力例 2

2


入力例 3

2
2 2
3 3
0 0
1 1


出力例 3

0


入力例 4

5
0 0
7 3
2 2
4 8
1 6
8 5
6 9
5 4
9 1
3 7


出力例 4

5


入力例 5

5
0 0
1 1
5 5
6 6
7 7
2 2
3 3
4 4
8 8
9 9


出力例 5

4


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