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<algorithm>
#include <cassert>
#include<string>
#include<vector>
#include <utility>
#include <math.h>
#include<cmath>
# include <set>
# include <iomanip>
# include <functional>
# include <queue>
#include<map>
#define INF 1000000009;
using namespace std;
int gcd(int a, int b) {
	while (a % b != 0) {
		int c = 0;
		c = a % b;
		a = b;
		b = c;
	}
	return  b;
}


int main() {
	int A[105],B[105],C[105];
	int hida = 0,   sita = 0;
	int tate=0,yoko=0,N = 0;
	cin >>yoko>>tate>> N;
	int migi = yoko;
	int ue = tate;
	for (int i = 0; i < N; i++) {
		cin >> A[i] >> B[i] >> C[i];
		if (C[i] == 1) {
			hida = max(hida, A[i]);
		}
		if (C[i] == 2) {
			migi = min(migi, A[i]);
		}
		if (C[i] == 3) {
			ue = min(ue, B[i]);
		}
		if (C[i] == 4) {
			
			sita = max(sita, B[i]);
		}
	}
	//cout << hida << endl << migi << endl << ue << endl << sita << endl;
	if ((migi - hida) <= 0||(ue-sita)<=0) {
		cout << '0' << endl;
		return 0;
	}
	cout << (migi - hida) * (ue - sita) << endl;
	return 0;
}