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

int main(void)
{
	int W, H, N;
	int i, j;
	int tateu, tates, yokom, yokoh;
	int menseki;
	
	scanf("%d %d %d", &W, &H, &N);
	int s[N][3];
	for (i = 0; i < N; i++)
	{
		for (j = 0; j < 3; j++)
			scanf("%d", &s[i][j]);
	}
	
	tateu = H;
	tates = 0;
	yokom = W;
	yokoh = 0;
		
	for (i = 0; i < N; i++)
	{
		switch (s[i][2])
		{
			case 1 : if (s[i][0] > yokoh); yokoh = s[i][0]; break;
			case 2 : if (yokom > s[i][0]); yokom = s[i][0]; break;
			case 3 : if (s[i][1] > tates); tates = s[i][1]; break;
			case 4 : if (tateu > s[i][1]); tateu = s[i][1]; break;
		}
	}
	
	menseki = (yokom - yokoh) * (tateu - tates);
	if (((yokom - yokoh) > 0) & ((tateu - tates) > 0))
		printf("%d\n", menseki);
	else
		printf("0\n");
	
	return 0;
}