200920: [AtCoder]ARC092 C - 2D Plane 2N Points

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

给定一个二维平面,上面分布着 $n$ 个红点和$n$ 个蓝点,其中第 $i$ 个红点的坐标为 $(a_i,b_i)$,第 $i$ 个蓝点的坐标为 $(c_i,d_i)$ 当一个红点的 $x$ 坐标严格小于一个蓝点的 $x$ 坐标,并且 $y$ 坐标严格小于这个蓝点的 $y$ 坐标时,这两个点可以成为一个 “好” 的点对 一个点只能属于一个 “好”的点对 求问最多有多少个“好”的点对

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