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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var
 n:longint;
 s:longint;
 map:array[1..210,1..210]of boolean;
 mark:array[1..210]of boolean;
 link:array[1..210]of longint;

procedure init;
var
 i,x,y,j:longint;
 a:array[1..210,1..2]of longint;
begin
 fillchar(map,sizeof(map),0);
 read(n);
 for i:=1 to n do
   readln(a[i,1],a[i,2]);
 for i:=1 to n do
  begin
   read(x,y);
   for j:=1 to n do
     if (x>a[j,1])and(y>a[j,2]) then begin map[j,i+n]:=true;  map[i+n,j]:=true; end;
  end;
 n:=n shl 1;
end;



function find(x:longint):boolean;
var
 i,q:longint;
begin
 for i:=1 to n do
  if map[x,i] and not mark[i] then
   begin
   q:=link[i]; link[i]:=x; mark[i]:=true;
   if (q=0) or find(q) then exit(true);
   link[i]:=q;
   end;
 exit(false);
end;



procedure main;
var
 i:longint;
begin
 s:=0;
 for i:=1 to n do
  begin
  fillchar(mark,sizeof(mark),false);
  if find(i) then inc(s);
  end;
 writeln(s shr 1);
 readln;
 readln;
end;

begin
 init;
 main;
end.