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>
#include <stdlib.h>

int main(void)
{
	int i,j,k;
	int w,h,n;
	int x[100] = {0}, y[100] = {0}, a[100] = {0};
	int s,sd,hs,hl,ws,wl;

	scanf("%d %d %d", &w, &h, &n);

	hs = 0;
	hl = h;
	ws = 0;
	wl = w;

	s = w * h;

	for(i = 0; i < n; i++)
	{
		scanf("%d %d %d", &x[i], &y[i], &a[i]);
	}

	for(i = 0; i < n; i++)
	{
		sd = 0;

		if (a[i] == 1 && x[i] > ws && x[i] < wl)
		{
			sd = (hl - hs) * (x[i] - ws);
			ws = x[i];

		}else if (a[i] == 2 && x[i] < wl && x[i] > ws)
		{
			sd = (hl - hs) * (wl - x[i]);
			wl = x[i];

		}else if (a[i] == 3 && y[i] > hs && y[i] < hl)
		{
			sd = (wl - ws) * (y[i] - hs);
			hs = y[i];

		}else if (a[i] == 4 && y[i] < hl && y[i] > hs)
		{
			sd = (wl - ws) * (hl - y[i]);
			hl = y[i];
		}

		s -= sd;

		if (s <= 0)
		{
			printf("0\n");
			return 0;
		}
	}

	printf("%d\n", s);



	return 0;
}