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>
#include <algorithm>
#include <map>
#include <set>
const int INF = 1e9;
#define FOR(i, a, n) for(int i = (int)(a); i < (int)(n); ++i)
#define REP(i, n) FOR(i, 0, n)
#define SORT(a) sort(a.begin(),a.end())
using namespace std;
int main(){
    int W,H,N,sum=0;
    cin >> W >> H >> N;

    int vec[W][H];
    REP(i,W){
        REP(j,H){
            vec[i][j] = 1;
        }
    }

    
    REP(i,N){
        int a,b,c;
        cin >> a >> b >>c;

        if(c==1){
            for(int j=0;j<a;j++){
                for(int k=0;k<H;k++){
                    vec[j][k] = 0;
                }
            }
        }else if(c==2){
            for(int j=a;j<W;j++){
                for(int k=0;k<H;k++){
                    vec[j][k] = 0;
                }
            }
        }else if(c ==3){
            for(int j=0;j<W;j++){
                for(int k=0;k<b;k++){
                    vec[j][k] = 0;
                }
            }
        }else {
            for(int j=0;j<W;j++){
                for(int k=b;k<H;k++){
                    vec[j][k] = 0;
                }
            }
        }

        REP(i,W){
            REP(j,H){
                sum += vec[i][j];
            }
        }
    }

    cout << sum << endl;
    

}