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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>
#include <ctime>
#include <algorithm>
#include <stdio.h>
#include <string>
#include <string.h>
#include <stdlib.h>
#include <sstream>
#include <vector>
#include <map>
#include <fstream>
using namespace std;

const int N = 100;

struct POINT{
	int x;
	int y;
	int a;
};
POINT mat[N];

int BOX[N + 1][N + 1];

int main()
{
	int W, H, n;

	cin >> W >> H >> n;

	for (int i = 0; i < n; i++) {
		cin >> mat[i].x >> mat[i].y >> mat[i].a;
	}


	for (int i = 0; i < n; i++) {
		switch (mat[i].a) {
		case 1:
			for (int j = 1; j <= H; j++) {
				for (int k = 1; k <= mat[i].x; k++) {
					BOX[j][k] = 1;
				}
			}
			break;
		case 2:
			for (int j = 1; j <= H; j++) {
				for (int k = mat[i].x + 1; k <= W; k++) {
					BOX[j][k] = 1;
				}
			}
			break;
		case 3:
			for (int j = 1; j < W; j++) {
				for (int k = 1; k <= mat[i].y; k++) {
					BOX[k][j] = 1;
				}
			}
			break;
		case 4:
			for (int j = 1; j <= W; j++) {
				for (int k = mat[i].y + 1; k <= H; k++) {
					BOX[k][j] = 1;
				}
			}
			break;
		}
	}

	int S = 0;
	for (int i = 1; i <= H; i++) {
		for (int j = 1; j <= W; j++) {
			if (BOX[i][j] == 0) {
				S++;
			}
		}
	}

	cout << S << endl;

	return 0;
}