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)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

N,d=gets.chomp.split(' ').map{|n| n.to_i}
RtoB = Array.new(N){[]}
BtoR = Array.new(N){[]}
R = Array.new(N)
B = Array.new(N)

0.upto(N-1){|i|
	x = gets.chomp.split(' ').map{|n| n.to_i}
	R[i] = x
}
0.upto(N-1){|i|
	x = gets.chomp.split(' ').map{|n| n.to_i}
	B[i] = x
}
0.upto(N-1){|i|
	rx = R[i]
	0.upto(N-1){|j|
		bx = B[j]
		if(rx[0] < bx[0] && rx[1] < bx[1])
			RtoB[i] << [j, bx]
			BtoR[j] << [i, rx]
		end
	}
}
dputs "RtoB"
dpp RtoB
dputs "BtoR"
dpp BtoR

sum = 0
RtoB_sorted = RtoB.sort{|a,b| a.size <=> b.size}
RtoB_sorted.each{|c|
	if(c.size != 0)
		selb = c.sort{|ibx1,ibx2| BtoR[ibx1[0]] <=> BtoR[ibx2[0]]}[0]
		selb_i = selb[0]
		dputs "selected : "
		dpp selb
		RtoB.each{|ibxlist|
			ibxlist.delete_if{|ibx| ibx[0] == selb_i}
		}
		sum += 1
	end
	ai = RtoB.find_index(c)
	BtoR.each{|irxlist|
		irxlist.delete_if{|irx| irx[0] == ai}
	}
	dputs "after selection of red #{ai}, "
	dputs "RtoB is "
	dpp RtoB
	dputs "BtoR is "
	dpp BtoR
}

puts sum