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>
#define MAX 105
using namespace std;
int a,x,y;
bool vis1[MAX], vis2[MAX],vis3[MAX],vis4[MAX];
int main() {
	int W, H, N,ans=0,black=0;
	cin >> W >> H >> N;
	ans = W * H;//1左2右3下4上
	for (int i = 1; i <= N; i++) {
		cin >>x>>y>>a;
		switch (a) {
		case 1:
			vis1[x] = 1;
			break;
		case 2:
			vis2[x] = 1;
			break;
		case 3:
			vis3[y] = 1;
			break;
		case 4:
			vis4[y] = 1;
			break;
		}
	}
	int max1, max2, max3, max4;
	max1 = max3 = 0;
	max2 = max4 = 999999;
	for (int i = 1; i <= W; i++) {
		if (vis1[i])
			max1 = max(i, max1);		
		if (vis3[i])
			max3 = max(i, max3);		
	}
	for (int i = 1; i <= H; i++) {
		if (vis2[i])
			max2 = min(i, max2);
		if (vis4[i])
			max4 = min(i, max4);
	}
	int w = 0, h = 0;
	if (max1 >= max2) {
		w = W;
	}
	else {
		max2 = max(0, W - max2);
		w = max1 + max2;
	}
	if (max3 >= max4) {
		h = H;
	}
	else {
		max4 = max(0, H - max4);
		h = max3 + max4;
	}
	//cout << max1 << " " << max2 << " " << max3 << " " << max4 << endl;
	//cout << w <<" " << h << endl;
	black = h*W +w*H  - (max1+max3)*(max2+max4);
	ans -= black;
	if (ans < 0) ans = 0;
	cout << ans << endl;
	return 0;
}