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 (2.7.1) (judge verdict: Wrong Answer)

#input of int(split by space)
def get_i()
  return gets.chomp.split(" ").map(&:to_i)
end
#input of float(split by space)
def get_f()
  return gets.chomp.split(" ").map(&:to_f)
end
#input of string(split by space)
def get()
  return gets.chomp.split(" ")
end
#input of string(split per one character)
def get_nsp()
  return gets.chomp.split("")
end
#yes or no decision
def yn_judge(bool,y="Yes",n="No")
  return bool ? y : n 
end
#create of array
def array(size1,init=nil,size2=-1)
  if size2==-1
      return Array.new(size1){init}
  else
      return Array.new(size2){Array.new(size1){init}}
  end
end

def max(a,b)
    return a>b ? a : b
end

def min(a,b)
    return a>b ? b : a
end

INF=Float::INFINITY

N=gets.to_i
ab=array(N)
N.times do|i|
    ab[i]=get_i
end
cd=array(N)
N.times do|i|
    cd[i]=get_i
end
def cal(ab,cd)
  ans=0
  visit=array(N,false)
    ab.each do|a,b|
    min_i=-1
    N.times do|i|
      if min_i==-1
          if a<cd[i][0] and b<cd[i][1] and not visit[i]
              min_i=i
          end
      else
          if a<cd[i][0] and b<cd[i][1] and not visit[i] and (cd[i][0]-a)**2+(cd[i][1]-b)**2<(cd[min_i][0]-a)**2+(cd[min_i][1]-b)**2
            min_i=i
          end
      end
    end
    unless min_i==-1
        ans+=1
        visit[min_i]=true
    end
  end
  return ans
end

res=[]
res<<cal(ab.sort{|x,y| x[0]<=>y[0]},cd)
res<<cal(ab.sort{|x,y| x[1]<=>y[1]},cd)
res<<cal(ab.sort{|x,y| y[0]<=>x[0]},cd)
res<<cal(ab.sort{|x,y| y[1]<=>x[1]},cd)
puts res.max