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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <stdio.h>

int main()
{
	int W,H,N,i,j,a[110],xy[110][2];
	scanf("%d",&W);
	scanf("%d",&H);
	scanf("%d",&N);
	
	for(i=0;i<N;i++){
		for(j=0;j<2;j++){
		scanf("%d",&xy[i][j]);
		}
		scanf("%d",&a[i]);
	}
	
	int x1=0,x2=W,y1=0,y2=H;
	
	for(i=0;i<N;i++){
		if(a[i]==1){
			if(xy[i][0]>x1){
				x1=xy[i][0];
			}
		}else if(a[i]==2){
			if(xy[i][0]<x2){
				x2=xy[i][0];
			}
		}else if(a[i]==3){
			if(xy[i][1]>y1){
				y1=xy[i][1];
			}
		}else {
			if(xy[i][1]<y2){
				y2=xy[i][1];
			}
			
		}
	}
	
	if(x1>=x2||y1>=y2){
		printf("\n0\n\n");
	}else {
		printf("\n%d\n\n",(x2-x1)*(y2-y1));
	}
	
	
	
	return 0;
}