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.to_i

field=Array.new(2*N){Array.new(2*N,:blank)}

N.times do
  x,y=gets.split.map(&:to_i)
  field[y][x]=:red
end
N.times do
  x,y=gets.split.map(&:to_i)
  field[y][x]=:blue
end
h={:red=>"R", :blank=>" ", :blue=>"B"}
#puts field.map{|arr| arr.map{|c| h[c] }.join(" ")}
#puts 

red_sum=Array.new(2*N){Array.new(2*N,0)}
(2*N).times do |y|
  red_sum[y][0]=  field[y][0]== :red ? 1 : 0
  (2*N-1).times do |x|
    red_sum[y][x+1]=red_sum[y][x]+ (field[y][x+1]== :red ? 1 : 0)
  end
end

(2*N).times do |x|
  (2*N-1).times do |y|
    red_sum[y+1][x]+=red_sum[y][x]
  end
end

#puts red_sum.map{|arr| arr.join(" ")}
#puts
blue_sum=Array.new(2*N){Array.new(2*N,0)}
(2*N).times do |y|
  blue_sum[y][0]=field[y][0]== :blue ? 1 : 0
  (2*N-1).times do |x|
    if field[y][x+1]== :blue
      blue_sum[y][x+1]=blue_sum[y][x]+ 1
    else
      blue_sum[y][x+1]=blue_sum[y][x]
    end
  end
end

(2*N).times do |x|
  (2*N-1).times do |y|
    blue_sum[y+1][x]+=blue_sum[y][x]#[pair_sum[y+1][x]+,red_sum[y][x+1]].min
  end
end
#puts blue_sum.map{|arr| arr.join(" ")}
#puts
m=-2*N
(2*N).times do |y|
  (2*N).times do |x|
    t=blue_sum[y][x]-red_sum[y][x]
    m=t if m<t
    #print t
    #print " "
  end
  #puts
end

puts N-m