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>
int main()
{
	int w,h,n,a,x,y,i,w0 = 0,h0 = 0,minw = 0,maxw,minh = 0,maxh,flag = 0;
	scanf("%d %d %d",&w,&h,&n);
	maxw = w;
	maxh = h;
	for(i = 0;i < n;i++)
	{
		scanf("%d %d %d",&x,&y,&a);
		if(a == 1)
		{
			if(minw < x)
			{
				w0 += x;
				minw = x;
			}
		}
		else if(a == 2)
		{
			if(maxw > x)
			{
				w0 += (w - x);
				maxw = x;
			}
		}
		else if(a == 3)
		{
			if(minh < y)
			{
				h0 += y;
				minh = y;
			}
		}
		else
		{
			if(maxh > y)
			{
				h0 += (h - y);
				maxh = y;
			}
		}
//		if(w0 >= w || h0 >= h)
//			flag = 1;
	}
	if(w0 < w && h0 < h /*&& flag == 0*/)
		printf("%d\n",(w - w0) * (h - h0));
	else
		printf("0\n");
	return 0;
}