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)

$n = gets().chomp!.to_i

small = []
$n.times { 
	x,y = gets().split.map{ |p|
		p.to_i
	}
	small <<[x,y]
}
big = []
$n.times { 
	x,y = gets().split.map{ |p|
		p.to_i
	}
	big <<[x,y]
}

$G = Array.new(2* $n)
0.upto(2* $n-1) do |i|
	$G[i] = []
end
# $G.each { |e| 
# 	e = 6  
# }
0.upto($n-1) do |i|
	0.upto($n-1) do |j|
		if small[i][0] < big[j][0] and  small[i][1] < big[j][1] then
			$G[i] << j+$n
			$G[j+$n] <<  i
		end
	end
end

$match = Array.new(2*$n, -1)
$used = Array.new(2*$n)

# p $G

# 増加パスをDFSでさがす
def dfs(v)
#	p v
#	p $used
	$used[v] = true
	$G[v].each do |jj|
		u = jj
		w = $match[u]
		if (w<0 || (!$used[w] && dfs(w)) )   then
			$match[v] = u
			$match[u] = v
#			puts "pair: #{u}, #{v}"
			return true
		end
	end
	return false
end

def bipa_match()
	res = 0

	$match.each do |pp|
		pp = -1
	end
	0.upto(2*$n-1) do |v|
		if $match[v] < 0 then
			# $used.each do |pp|
			# 	pp = false
			# end
			0.upto(2*$n - 1) do |kk|
				$used[kk] = false
			end
			if dfs(v) then
				res+=1
#				p $match
			end
		end
	end
return res

end

puts bipa_match()