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 <bits/stdc++.h>
#define INF LLONG_MAX
#define ll  long long
#define ull unsigned long long
#define rep(i,n) for(int i=0; i<n; ++i)
#define MOD 1000000007
using namespace std;
template<class T> inline bool chmin(T& a, T b) { if(a>b) {a=b; return true;} return false;}
template<class T> inline bool chmax(T& a, T b) { if(a<b) {a=b; return true;} return false;}

int main() {
  int W,H,N; cin >> W >> H >> N;
  vector<int> x(N), y(N), a(N);
  rep(i,N) cin >> x[i] >> y[i] >> a[i];
  int x0=0, x1=W, y0=0, y1=H;
  rep(i,N) {
    switch(a[i]) {
      case 1:
        if(x0 <= x[i]) x0 = x[i];
        break;
      case 2:
        if(x1 >= x[i]) x1 = x[i];
        break;
      case 3:
        if(y0 <= y[i]) y0 = y[i];
        break;
      case 4:
        if(y1 >= y[i]) y1 = y[i];
        break;
    }
  }
  int area = (x1-x0)*(y1-y0);
  printf("%d\n", area<0?0:area);
}