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 Dinic
  def initialize(v, inf = 2**30)
    @V = v
    @inf = inf
    @g = Array.new(v) {[]}
    @level = Array.new(v, 0)
    @iter = Array.new(v, 0)
  end
  attr_accessor :g

  def add_edge(from, to, cap)
    @g[from] << {"to" => to, "cap" => cap, "rev" => @g[to].size}
    @g[to] << {"to" => from, "cap" => 0, "rev" => @g[from].size-1}
  end

  def bfs(s) # sからの最短距離をbfs
    @level = Array.new(@V, -1)
    @level[s] = 0
    q = [s]
    while !q.empty?
      v = q.shift
      @g[v].size.times do |i|
        e = @g[v][i]
        if e["cap"] > 0 && @level[e["to"]] < 0
          @level[e["to"]] = @level[v] + 1
          q << e["to"]
        end
      end
    end
  end

  def dfs(v, t, f)
    return f if v == t
    (@iter[v]...@g[v].size).each do |i|
      @iter[v] = i
      e = @g[v][i]
      if e["cap"] > 0 && @level[v] < @level[e["to"]]
        d = dfs(e["to"], t, [f, e["cap"]].min)
        if d > 0
          e["cap"] -= d
          @g[e["to"]][e["rev"]]["cap"] += d
          return d
        end
      end
    end
    return 0
  end

  def max_flow(s, t)
    flow = 0
    while true
      bfs(s)
      return flow if @level[t] < 0
      @iter = Array.new(@V, 0)
      f = dfs(s, t, @inf)
      while f > 0
        flow += f
        f = dfs(s, t, @inf)
      end
    end
  end
end


N = gets.to_i
g = Dinic.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)