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: Wrong Answer)

N = gets.chomp.to_i

red = []
N.times do
  x, y = gets.chomp.split(" ").map(&:to_i)
  red << {x: x, y: y}
end

blue = []
N.times do
  x, y = gets.chomp.split(" ").map(&:to_i)
  blue << {x: x, y: y}
end

count_candidates = []
red.each_with_index do |r, idx|
  candidates = blue.select {|b| b[:x] >= r[:x] and b[:y] >= r[:y]}
  count_candidates[idx] = candidates.size
end

z = red.zip(count_candidates).sort do |a, b|
  a[1] <=> b[1]
end
z = z.map {|t| t[0]}

def recur(red, r_idx, blue, result)
  return result if r_idx >= red.size

  r = red[r_idx]
  candidates = blue.select {|b| b[:x] >= r[:x] and b[:y] >= r[:y]}

  list = [0]
  candidates.each do |b|
    t = blue.clone
    t.delete(b)
    list << recur(red, r_idx + 1, t, result + 1)
  end
  list.max
end

puts recur(z, 0, blue, 0)