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)

n = gets.chomp.to_i
def get_points(n)
  (0...n).map do |i|
    a = gets.chomp.split(' ').map(&:to_i)
    { index: i, x: a[0], y: a[1] }
  end
end
reds = get_points(n)
blues = get_points(n)

pairable_blues_by_red = reds.map do |red|
  blues.find_all do |blue|
    red[:x] < blue[:x] && red[:y] < blue[:y]
  end
end

blue_use_checklist = Array.new(n, false)
def max_pairs_count(pairable_blues_by_red, blue_use_checklist)
  pairable_blues = pairable_blues_by_red[0]

  if pairable_blues_by_red.count == 1
    if pairable_blues.any? { |blue| !blue_use_checklist[blue[:index]] }
      return 1
    else
      return 0
    end
  end
  rest = pairable_blues_by_red.slice(1, pairable_blues_by_red.count - 1)

  usable_blues =
    pairable_blues.find_all{ |blue| !blue_use_checklist[blue[:index]] }
  if usable_blues.count == 0
    return max_pairs_count(rest, blue_use_checklist)
  end

  pairs_count_by_blue = usable_blues.map do |blue|
    blue_use_checklist[blue[:index]] = true
    max_pairs_count_about_rest =
      max_pairs_count(rest, blue_use_checklist)
    blue_use_checklist[blue[:index]] = false
    1 + max_pairs_count_about_rest
  end
  return pairs_count_by_blue.max
end
puts max_pairs_count(pairable_blues_by_red, blue_use_checklist)