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 <bits/stdc++.h>
using namespace std;

int a1[105],a2[105],a3[105],a4[105],c1,c2,c3,c4;
int w,h,q;
int x,y,a;

int main(){
	cin >> w >> h >> q;
	for(int i=0; i<q; i++){
		cin >> x >> y >> a;
		if(a==1)
			a1[c1++] = x;
		if(a==2)
			a2[c2++] = x;
		if(a==3)
			a3[c3++] = y;
		if(a==4)
			a4[c4++] = y;
	}
	sort(a1,a1+c1),sort(a2,a2+c2),sort(a3,a3+c3),sort(a4,a4+c4);
	int x1,x2,y1,y2;
	x1 = a1[c1-1],x2 = a2[0];
	y1 = a3[c3-1],y2 = a4[0];
	// cout << x1 << " " << x2 << " " << y1 << " " << y2 << endl;
	if(c2 == 0) x2 = w;
	if(c4 == 0) y2 = h;
	if(x2-x1<=0 || y2-y1<=0)
		cout << "0" << endl;
	else
		cout << (x2-x1)*(y2-y1) << endl;

}