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)

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

int main(void)
{
    
    int W,H;
    int N;
    int x[100];
    int y[100];
    int n[100];
    int f[100][100];
    
    int cnt=0;
    
    scanf("%d %d %d",&W,&H,&N);
    
    
    for (int i=0; i<N; i++) {
        
        scanf("%d %d %d",&x[i],&y[i],&n[i]);
        
    }
    for (int i=0; i<100; i++) {
        for (int j=0; j<100; j++) {
            
            f[i][j]=0;
        }
        
    }
    
    
    
    for (int i=0; i<N; i++) {
        if (n[i]==1) {
            for (int Y=0; Y<H; Y++) {
                
            for (int X=0; X<x[i]; X++) {
                
                f[X][Y]=1;
                
            }
            }
            
            
        }
        if (n[i]==2) {
            for (int Y=0; Y<H; Y++) {
                
                for (int X=x[i]; X<W; X++) {
                    
                    f[X][Y]=1;
                    
                }
            }

            
            
        }
        if (n[i]==3) {
            for (int Y=0; Y<y[i]; Y++) {
                
                for (int X=0; X<W; X++) {
                    
                    f[X][Y]=1;
                    
                }
            }
            
            
        }
        if (n[i]==4) {
            for (int Y=y[i]; Y<H; Y++) {
                
                for (int X=0; X<W; X++) {
                    
                    f[X][Y]=1;
                    
                }
            }
            
            
        }
        
    
    }
    
    
    for (int i=0; i<W; i++) {
        for (int j=0; j<H; j++) {
            if(f[i][j]==0){
                
                cnt++;
                
            }
        }
        
    }
    
    printf("%d\n",cnt);
    
    
   
    
    
    
  
    
    return 0;
}