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)

def draw(arr)
  puts "--"
  puts arr.map{|row| row.map(&:to_s).join(' ')}
end

N=gets.to_i
field = Array.new(2*N) {Array.new(2*N, '.')}
N.times do
  a,b = gets.split.map(&:to_i)
  field[b][a] = 'R'
end
N.times do
  a,b = gets.split.map(&:to_i)
  field[b][a] = 'B'
end

# cnt[y][x]
cnt_red = Array.new(2*N) {Array.new(2*N, 0)}
(2*N).times do |y|
  (2*N).times do |x|
    if y-1 >= 0 && x-1 >= 0
      cnt_red[y][x] = cnt_red[y-1][x] + cnt_red[y][x-1] - cnt_red[y-1][x-1] + (field[y][x] == 'R' ? 1 : 0)
    elsif y-1 >= 0
      cnt_red[y][x] = cnt_red[y-1][x] + (field[y][x] == 'R' ? 1 : 0)
    elsif x-1 >= 0
      cnt_red[y][x] = cnt_red[y][x-1] + (field[y][x] == 'R' ? 1 : 0)
    else
      cnt_red[y][x] = (field[y][x] == 'R' ? 1 : 0)
    end
  end
end

# cnt[y][x]
cnt_blue = Array.new(2*N) {Array.new(2*N, 0)}
(2*N).times do |y|
  (2*N).times do |x|
    if y-1 >= 0 && x-1 >= 0
      cnt_blue[y][x] = cnt_blue[y-1][x] + cnt_blue[y][x-1] - cnt_blue[y-1][x-1] + (field[y][x] == 'B' ? 1 : 0)
    elsif y-1 >= 0
      cnt_blue[y][x] = cnt_blue[y-1][x] + (field[y][x] == 'B' ? 1 : 0)
    elsif x-1 >= 0
      cnt_blue[y][x] = cnt_blue[y][x-1] + (field[y][x] == 'B' ? 1 : 0)
    else
      cnt_blue[y][x] = (field[y][x] == 'B' ? 1 : 0)
    end
  end
end

ans = Array.new(2*N) {Array.new(2*N, 0)}
(2*N).times do |y|
  (2*N).times do |x|
    if y-1 >= 0 && x-1 >= 0
      ans[y][x] = ans[y-1][x] + ans[y][x-1] - ans[y-1][x-1] + (cnt_blue[y][x] <= cnt_red[y][x] && field[y][x] == 'B'  ? 1 : 0)
    elsif y-1 >= 0
      ans[y][x] = ans[y-1][x] + (cnt_blue[y][x] <= cnt_red[y][x] && field[y][x] == 'B'  ? 1 : 0)
    elsif x-1 >= 0
      ans[y][x] = ans[y][x-1] + (cnt_blue[y][x] <= cnt_red[y][x] && field[y][x] == 'B'  ? 1 : 0)
    else
      ans[y][x] = (cnt_blue[y][x] <= cnt_red[y][x] && field[y][x] == 'B'  ? 1 : 0)
    end
  end
end
# draw(field.reverse)
# draw(cnt_red.reverse)
# draw(cnt_blue.reverse)
# draw(ans.reverse)
puts ans[-1][-1]