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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
int main(){
  int W,H,N;
  scanf("%d%d%d",&W,&H,&N);
  int x[N],y[N],a[N];
  int i;
  for(i=0;i<N;i++){
    scanf("%d%d%d",&x[i],&y[i],&a[i]);
  }
  int x1=0;
  int x2=0;
  int y1=0;
  int y2=0;
  for(i=0;i<N;i++){
    if(a[i]==1){
      if(x1<x[i]){
        x1=x[i];
      }
    }
    else if(a[i]==2){
      if(x2<x[i]){
        x2=x[i];
      }
    }
    else if(a[i]==3){
      if(y1<y[i]){
        y1=y[i];
      }
    }
    else{
      if(y2<y[i]){
        y2=y[i];
      }
    }
  }
  int num1,num2;
  if(x2!=0){
    W=x2;
  }
  if(y2!=0){
    H=y2;
  }
  num1=W-x1;
  num2=H-y1;
  printf("%d\n",num1);
  printf("%d\n",num2);
  if(num1>0&&num2>0){
    printf("%d",num1*num2);
  }
  else{
    printf("%d",0);
  }
}