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 <vector>

using namespace std;

int main(){
    int W, H, N;
    cin >> W >> H >> N;
    vector<int> x(N), y(N), a(N);
    for(int i = 0; i < N; i++){
        cin >> x[i] >> y[i] >> a[i];
    }
    // 白:1　黒:0
    vector< vector<int> > sq(W, vector<int>(H, 1));

    for (int i = 0; i < N; i++)
    {
        switch (a[i])
        {
        case 1:
            for (int j = 0; j < x[i]; j++)
            {
                for (int k = 0; k < H; k++)
                {
                    sq[j][k] = 0;
                }
            }
            break;
        case 2:
            for (int j = x[i]; j < W; j++)
            {
                for (int k = 0; k < H; k++)
                {
                    sq[j][k] = 0;
                }
            }
            break;
        case 3:
            for (int j = 0; j < W; j++){
                for (int k = 0; k < y[i]; k++){
                    sq[j][k] = 0;
                }
            }
                break;
        case 4:
            for (int j = 0; j < W; j++){
                for (int k = y[i]; k < H; k++){
                    sq[j][k] = 0;
                }
            }
            break;
        default:
            break;
        }
    }

    int x_min = W, x_max = -1;
    int y_min = H, y_max = -1;

    for (int i = 0; i < W; i++)
    {
        for (int j = 0; j < H; j++){
            if(sq[i][j] == 1){
                if(i < x_min)
                    x_min = i;
                if(i > x_max)
                    x_max = i;
                break;
            }
        }
    }

    for (int i = 0; i < H; i++){
        for (int j = 0; j < W; j++){
            if (sq[j][i] == 1)
            {
                if(i < y_min)
                    y_min = i;
                if (i > y_max)
                    y_max = i;
                break;
            }
        }
    }

    cout << "x_min " << x_min << "x_max " << x_max << endl;
    cout << "y_min " << y_min << "y_max " << y_max << endl;

    int area;
    if(x_min == W || x_max == -1 || y_min == H || y_max == -1)
        area = 0;
    else area = (x_max - x_min + 1) * (y_max - y_min + 1);
    
    cout << area << endl;
    
}