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 9.2.1) (judge verdict: Accepted)

int main(void){

  int W,H,N,i,j,k,x[100],y[100],a[100];
  int size=0;
  int mat[100][100];
  scanf("%d %d %d",&W,&H,&N);
  for(i=0;i<N;i++){
  	scanf(" %d %d %d",&x[i],&y[i],&a[i]);
  }
  
  for(i=0;i<W;i++){
  	for(j=0;j<H;j++){
    	mat[i][j]=0;//white
    }
  }
  
  for(i=0;i<N;i++){
    if(a[i]==1){
    	for(j=0;j<x[i];j++){
          for(k=0;k<H;k++){
        	mat[j][k]=1;
          }
        }
    }
    else if(a[i]==2){
    	for(j=x[i];j<W;j++){
          for(k=0;k<H;k++){
        	mat[j][k]=1;
          }
    	}
  	}
    else if(a[i]==3){
    	for(j=0;j<W;j++){
          for(k=0;k<y[i];k++){
        	mat[j][k]=1;
          }
        }
    }
    else if(a[i]==4){
    	for(j=0;j<W;j++){
          for(k=y[i];k<H;k++){
        	mat[j][k]=1;
          }
        }
    }
  }
  
  for(i=0;i<W;i++){
  	for(j=0;j<H;j++){
    	if(mat[i][j]==0){
        	size++;
        }
    }
  }
  
  printf("%d\r\n",size);
  
  return 0;
}