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: Time Limit Exceeded)

def reductant_relationship(relationships, number)
  relationships.map {|line| line.select {|num| num!=number }}[1..-1]
end

def recursion_count(relationships, count)
  current_relationships = relationships.reject(&:empty?)
  return count if current_relationships.flatten.empty?

  current_relationships[0].map {|e| recursion_count(reductant_relationship(current_relationships, e), count+1) }.max
end

lines = readlines.map(&:strip)

n = lines[0].to_i
red_points = lines[1..n].map{|e|e.split.map(&:to_i)}
blue_points = lines[n+1..n*2].map{|e|e.split.map(&:to_i)}


red_blue = []
for red_point in red_points
  line = blue_points.map.with_index { |blue_point, index|
    index if(blue_point[0] > red_point[0] && blue_point[1] > red_point[1])
  }
  red_blue.push line.compact
end

#puts red_points.inspect
#puts blue_points.inspect
# puts red_blue.inspect

puts recursion_count(red_blue, 0)