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)

//
//  main.cpp
//  leetcode
//
//  Created by caokai on 2016/11/23.
//  Copyright © 2016年 caokai. All rights reserved.
//

#include <cstdlib>
#include <algorithm>
#include <list>
#include <string>
#include <vector>
#include <cstdio>
using namespace std;
struct region {
    region (int w, int h): w(w), h(h), regions(h, vector<int>(w, 0)){}
    int w, h;
    vector<vector<int>> regions;
    void change (int i, int xi, int yi) {
        switch (i) {
                case 1:
                for (auto & ve: regions) for (int j = 0; j < xi; j++) ve[j] = 1;
                break;
            case 2:
                for (auto & ve: regions) for (int j = xi; j < ve.size(); j++) ve[j] = 1;
                break;
                case 3:
                for (int j = 0; j < yi; j++) regions[j] = vector<int>(w, 1);
                break;
                case 4:
                for (int j = yi; j < h; j++) regions[j] = vector<int>(w, 1);
                break;
        }
    }
    int count() {
        int sum = 0;
        for (auto & ve: regions) for (auto in: ve) sum += in;
        return w * h -sum;
    }
};
int main(int argc, const char * argv[]) {
    int w, h, n;
    scanf("%d %d %d", &w, &h, &n);
    region test(w, h);
    while( n--) {
        int x, y, z;
        scanf("%d %d %d", &x, &y, &z);
        test.change(z, x, y);
    }
    printf("%d\n", test.count());
    return 0;
}