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 (Clang 3.8.0) (judge verdict: Accepted)

#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
using namespace std;

int main(int argc, const char * argv[]) {

    // cinを高速にするためのおまじない
    cin.tie(0);
    ios::sync_with_stdio(false);

    /////////////////////
    // Write code below /
    /////////////////////
    int result = 0;
    int W, H, N;
    cin >> W >> H >> N;
    vector<int> xList;
    vector<int> yList;
    vector<int> aList;
    for(int i=0; i<N; i++) {
        int x;
        int y;
        int a;
        cin >> x >> y >> a;
        xList.push_back(x);
        yList.push_back(y);
        aList.push_back(a);
    }
    int a1MaxX = -1;
    int a2MinX = 101;
    int a3MaxY = -1;
    int a4MinY = 101;
    for(int i=0; i<N; i++) {
        int x = xList[i];
        int y = yList[i];
        int a = aList[i];
        if (a == 1) {
            if (x > a1MaxX) {
                a1MaxX = x;
            }
        } else if (a == 2) {
            if (x < a2MinX) {
                a2MinX = x;
            }
        } else if (a == 3) {
            if (y > a3MaxY) {
                a3MaxY = y;
            }
        } else {
            if (y < a4MinY) {
                a4MinY = y;
            }
        }
    }
    int whiteW = W;
    int whiteH = H;
    if (a1MaxX != -1) {
        whiteW -= a1MaxX;
    }
    if (a2MinX != 101) {
        whiteW -= (W - a2MinX);
    }
    if (a3MaxY != -1) {
        whiteH -= a3MaxY;
    }
    if (a4MinY != 101) {
        whiteH -= (H - a4MinY);
    }
    if (whiteW < 0) {
        whiteW = 0;
    }
    if (whiteH < 0) {
        whiteH = 0;
    }
    result = whiteW * whiteH;
    if (result < 0) {
        result = 0;
    }
    cout << result;

    return 0;
}