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 OCaml (4.02.3) (judge verdict: Accepted)

let rec list_init n f = if n <= 0 then [] else let x = f () in x :: list_init (n-1) f
let rec remove x = function [] -> [] | (y::ys') -> if x = y then ys' else y :: remove x ys'
let step (acc, zs) (x,y) =
  match List.filter (fun (a,b) -> a < x && b < y) zs with
  | []     -> (acc,   zs)
  | (z::_) -> (acc+1, remove z zs)
let () =
  Scanf.scanf "%d" (fun n ->
  let a = list_init n (fun _ -> Scanf.scanf " %d %d" (fun x y -> x, y))
  |> List.sort (fun (_,b) (_,d) -> d - b) in
  list_init n (fun _ -> Scanf.scanf " %d %d" (fun x y -> x, y))
  |> List.sort compare |> List.fold_left step (0, a)) |> fst |> Printf.printf "%d\n"