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 Ruby (2.3.3) (judge verdict: Accepted)

n = gets.to_i
ps = (2*n).times.map{ gets.split.map(&:to_i)}
rel = Array.new(2*n+2){[]}
(n...2*n).each{|i|
    n.times{|j|
        if ps[j][0]<ps[i][0] and ps[j][1]<ps[i][1]
           rel[j] << i
        end
    }
    rel[i] << 2*n+1
}
n.times{|i| rel[2*n] << i}
visited = []

find = ->i{
    return [i] if i==2*n+1
    rel[i].each{|j|
        unless visited[j]
            visited[j] = true
            tmp = find[j]
            if tmp
               tmp << i
               return tmp
            end
        end
    }
    return nil
}

retain = ->a{
    a.each_cons(2){|i,j|
        rel[i] << j
        rel[j].delete(i)
    }
}

res = 0
loop{
    seq = find[2*n]
    break unless seq
    visited = []
    retain[seq]
    res += 1
}
p res