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)

#define _USE_NATH_DEFINES
#include<cstdio>
#include <iostream>
#include<sstream>
#include<fstream>
#include<iomanip>
#include<algorithm>
#include<cmath>
#include<complex>
#include <string>
#include<vector>
#include<list>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<bitset>
#include<numeric>
#include<limits>
#include<climits>
#include<cfloat>
#include<functional>
#include<iterator>
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)
using namespace std;

int main() {
	int w, h, n;
	cin >> w >> h >> n;
	int x[150], y[150], a[150];
	rep(i, n) cin >> x[i] >> y[i] >> a[i];
	int s = 0, t = 0, u = 0, v = 0;
	bool x_exit = false, y_exit = false;
	vector<int> tt, vv;
	rep(i, n) {
		if (a[i] == 1) {
			s = max(s, x[i]);
		}
		else if (a[i] == 2) {
			//t = min(t, x[i]);
			tt.push_back(x[i]);
			x_exit = true;
		}
		else if (a[i] == 3) {
			u = max(u, y[i]);
		}
		else if (a[i] == 4) {
			//v = min(v, y[i]);
			vv.push_back(y[i]);
			y_exit = true;
		}
	}
	if (x_exit) {
		sort(tt.begin(), tt.end());
		t = w - tt[0];
	}
	if (y_exit) {
		sort(vv.begin(), vv.end(), greater<int>());
		v = h- vv[0];
	}
	int ans = (w - s - t)*(h - u - v);
	if(ans > 0) cout << ans << endl;
	else cout << 0 << endl;
	return 0;
}