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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

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

#define println(msg) cout << msg << endl
#define yes_or_no(flag) if (flag) { println("Yes"); } else { println("No"); }
#define sort_vec(vec) sort(vec.begin(), vec.end())
#define rsort_vec(vec) sort(vec.rbegin(), vec.rend()) // greater<int>()

int main() {
  // 入力
  int W, H, N;
  cin >> W >> H >> N;

  vector<tuple<int, int, int>> d(N);
  for (int i = 0; i < N; i++) {
    int x, y, a;
    cin >> x >> y >> a;
    d.at(i) = make_tuple(x, y, a);
  }
  
  // 計算
  int xmin = 0;
  int xmax = W;
  int ymin = 0;
  int ymax = H;
  
  for (int i = 0; i < N; i++) {
    int a = get<2>(d.at(i));
    switch (a) {
      case 1: // x < xi
        xmin = get<0>(d.at(i));
        break;
      case 2: // x > xi
        xmax = get<0>(d.at(i));
        break;
      case 3: // y < yi
        ymin = get<1>(d.at(i));
        break;
      case 4: // y > yi
        ymax = get<1>(d.at(i));
        break;
    }
  }
  //
  if (xmin > xmax) {
	println(0);
    return 0;
  }
  
  if (ymin > ymax) {
	println(0);
    return 0;
  }
  
  // 出力
  println((xmax - xmin) * (ymax - ymin));
}