Problem:
Score : 200 points

Problem Statement

There is a rectangle in the xy-plane, with its lower left corner at (0, 0) and its upper right corner at (W, H). Each of its sides is parallel to the x-axis or y-axis. Initially, the whole region within the rectangle is painted white.

Snuke plotted N points into the rectangle. The coordinate of the i-th (1 ≦ i ≦ N) point was (x_i, y_i).

Then, he created an integer sequence a of length N, and for each 1 ≦ i ≦ N, he painted some region within the rectangle black, as follows:

If a_i = 1, he painted the region satisfying x < x_i within the rectangle.

If a_i = 2, he painted the region satisfying x > x_i within the rectangle.

If a_i = 3, he painted the region satisfying y < y_i within the rectangle.

If a_i = 4, he painted the region satisfying y > y_i within the rectangle.

Find the area of the white region within the rectangle after he finished painting.

Constraints

1 ≦ W, H ≦ 100

1 ≦ N ≦ 100

0 ≦ x_i ≦ W (1 ≦ i ≦ N)

0 ≦ y_i ≦ H (1 ≦ i ≦ N)

W, H (21:32, added), x_i and y_i are integers.

a_i (1 ≦ i ≦ N) is 1, 2, 3 or 4.

Input

The input is given from Standard Input in the following format:

W H N
x_1 y_1 a_1
x_2 y_2 a_2
:
x_N y_N a_N

Output

Print the area of the white region within the rectangle after Snuke finished painting.

Sample Input 1

5 4 2
2 1 1
3 3 4

Sample Output 1

9

The figure below shows the rectangle before Snuke starts painting.

First, as (x_1, y_1) = (2, 1) and a_1 = 1, he paints the region satisfying x < 2 within the rectangle:

Then, as (x_2, y_2) = (3, 3) and a_2 = 4, he paints the region satisfying y > 3 within the rectangle:

Now, the area of the white region within the rectangle is 9.

Sample Input 2

5 4 3
2 1 1
3 3 4
1 4 2

Sample Output 2

0

It is possible that the whole region within the rectangle is painted black.

Sample Input 3

10 10 5
1 6 1
4 1 3
6 9 4
9 4 2
3 1 3

Sample Output 3

64

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

/*
  B - すぬけ君の塗り絵 2 イージー / Snuke's Coloring 2 (ABC Edit)
  <http://abc047.contest.atcoder.jp/tasks/abc047_b>
*/

#include <stdio.h>
#include <stdlib.h>

int main(int argc, char const *argv[]) {
  int W, H, N;
  int x, y, a;
  int w0, w1, h0, h1;
  int i;

  scanf("%d %d %d", &W, &H, &N);
  w0 = 0;
  w1 = W;
  h0 = 0;
  h1 = H;

  for( i=0; i<N; i++ ){
    scanf("%d %d %d", &x,&y,&a );
    if( (a==1)&&(x>w0) ) w0 = x;
    if( (a==2)&&(x<w1) ) w1 = x;
    if( (a==3)&&(y>h0) ) h0 = y;
    if( (a==4)&&(y<h1) ) h1 = y;
  }
  if( ((w1-w0)<0) || ((h1-h0)<0) ){
    printf("%d\n", 0);
  }else{
    printf( "%d\n", (w1-w0)*(h1-h0) );
  }

  return 0;
}