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: Accepted)

#include <iostream>
#include<algorithm>
#include<string>
#include<vector>
#define _USE_MATH_DEFINES
#include <math.h>
#include <iomanip>
#include <stdio.h>
#include <numeric>
#include <cmath>
#include <limits>
#include <bitset> 
using namespace std;


int main()
{
	int w, h, n,maxX=0,minX=10000,maxY=0,minY=100000;
	cin >> w >> h >> n;
	vector<int>x(n),y(n),a(n);
	for (int i = 0; i < n; i++)cin >> x[i] >> y[i] >> a[i];
	x.push_back(w);
	y.push_back(0);
	a.push_back(2);
	x.push_back(0);
	y.push_back(h);
	a.push_back(4);
	for (int i = 0; i < a.size(); i++) {
		switch (a[i]) {
			case 1:maxX = max(maxX, x[i]); break;
			case 2:minX = min(minX, x[i]); break;
			case 3:maxY = max(maxY, y[i]); break;
			case 4:minY = min(minY, y[i]); break;
		}
	}
	cout << (minX-maxX)*(minY-maxY)*(minX>maxX && minY>maxY) << endl;
}