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: Wrong Answer)

#include<stdio.h>
#define MAX 100

int main(){
  int x1=0,x2=0,x3,x4,y1=0,y2,y3=0,y4,i=0,t,L[MAX];
  for(int i=0;i<3;i++){
    scanf("%d",&L[i]);
  }
  x3=x4=L[0];
  y2=y4=L[1];
  t=L[2];
  for(i=0;i<t;i++){
    for(int j=0;j<3;j++){
      scanf("%d",&L[j]);
    }
    switch(L[2]){
      case 1:
      if(x1<L[0]){
      x1=x2=L[0];
      }
      break;
      case 2:
      if(x3>L[0]){
      x3=x4=L[0];
      }
      break;
      case 3:
      if(y1<L[1]){
      y1=y3=L[1];
      }
      break;
      case 4:
      if(y2>L[1]){
      y2=y4=L[0];
      }
      break;
    }
  }
  if((x3-x1)*(y4-y1)<0){
    printf("0");
  }else{
    printf("%d",(x3-x1)*(y4-y1));
  }
  return 0;
}