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)

#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <stack>
#include <queue>
#include <cctype>
#define rep(i, m, n) for(int i = m;i < n;i++)
#define repr(i, n) for(int i = n;i >= 0;i--)
#define ll long long
#define ull unsigned long long
#define push(a) push_back(a)
#define pop(a) pop_back(a)
#define debug(x) cout<<#x<<": "<<x<<endl
#define SORT(v, n) sort(v, v+n);
#define VSORT(v) sort(v.begin(), v.end());
#define INF 999999999
using namespace std;
typedef pair<int, int> P;
typedef pair<ll, ll> LP;
typedef pair<int, P> PP;
typedef pair<ll, LP> LPP;

int dy[]={0, 0, 1, -1, 0};
int dx[]={1, -1, 0, 0, 0};

int main(){
  int w,h,n,x[101],y[101],a[101],cnt=0;
  bool sq[101][101]={};
  cin >> w >> h >> n;
  rep(i,0,n){
    cin >> x[i] >> y[i] >> a[i];
  }
  rep(i,0,n){
    if(a[i]==1){
      rep(j,0,h){
        rep(k,0,x[i]){
          sq[j][k] = true;
        }
      }
    }else if(a[i]==2){
      rep(j,0,h){
        rep(k,x[i],w){
          sq[j][k] = true;
        }
      }
    }else if(a[i]==3){
      rep(j,0,y[i]){
        rep(k,0,w){
          sq[j][k] = true;
        }
      }
    }else{
      rep(j,y[i],h){
        rep(k,0,w){
          sq[j][k] = true;
        }
      }
    }
  }

  rep(i,0,h){
    rep(j,0,w){
      if(sq[i][j]==0) cnt++;
    }
  }
  cout << cnt << endl;
}