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)

class EdmondsKarp
  def initialize(n)
    @n = n
    @flow = Array.new(n) { Array.new(n, 0) }
    @cap = Array.new(n) { Array.new(n, 0) }
  end

  def add_edge(s, t, w)
    @cap[s][t] = w
  end

  def max_flow(start, goal)
    inf = 2 ** 30
    sum = 0
    while true
      que = [start]
      prev = Array.new(@n, -1)
      prev[start] = start
      while !que.empty? && prev[goal] == -1
        u = que.shift
        @n.times do |i|
          if prev[i] == -1 && @cap[u][i] - @flow[u][i] > 0
            prev[i] = u
            que.push(i)
          end
        end
      end
      return sum if (prev[goal] == -1)
      inc = inf
      c = goal
      while c != start
        inc = [inc, @cap[prev[c]][c] - @flow[prev[c]][c]].min
        c = prev[c]
      end
      c = goal
      while c != start
        @flow[prev[c]][c] += inc
        @flow[c][prev[c]] -= inc
        c = prev[c]
      end
      sum += inc
    end
  end
end


N = gets.to_i
g = EdmondsKarp.new(2*N+2)
s = 2*N
t = s + 1

red = {}
blue = {}

N.times do |i|
  g.add_edge(s, i, 1)
  red[i] = gets.split.map(&:to_i)
end
N.times do |i|
  g.add_edge(N+i, t, 1)
  blue[N+i] = gets.split.map(&:to_i)
end
N.times do |i|
  N.times do |j|
    if red[i][0] < blue[N+j][0] && red[i][1] < blue[N+j][1]
      g.add_edge(i, N+j, 1)
    end
  end
end

puts g.max_flow(s, t)