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<bits/stdc++.h>
using namespace std;
#define ALL(v) (v).begin(),(v).end()
#define REP(i,p,n) for(int i=p;i<(int)(n);++i)
#define rep(i,n) REP(i,0,n)
#define SZ(x) ((int)(x).size())
#define debug(x) cerr << #x << ": " << x << '\n'
#define INF 999999999
typedef long long int Int;
typedef pair<int,int> P;
using ll = long long;
using VI = vector<int>;


int main(){
  int w,h,n;cin >> w >> h >> n;
  int a[h][w]={0};
  /*auto print = [&](){
    rep(i,h){
      rep(j,w){
        cout << a[i][j];
      }
      cout << endl;
    }
  };*/
  for(int k=0;k<n;k++){
    int x,y,comand;
    cin >> x >> y >> comand;
    int bx,ex,by,ey;
    if(comand==1){
      bx = 0;
      by = 0;
      ex = x;
      ey = h;
    }
    else if(comand==2){
      bx= x;
      ex = w;
      by = 0;
      ey = h;
    }
    else if(comand==3){
      bx = 0;
      ex = w;
      by = 0;
      ey = y;
    }
    else{
      bx = 0;
      ex = w;
      by = y;
      ey = h;
    }
    REP(s,by,ey){
      REP(t,bx,ex){
        a[s][t] = 1;
      }
    }
  }
  int ans = 0;
  rep(i,h)rep(j,w){
    if(a[i][j]!=1)ans++;
  }
  cout << ans << endl;
}