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 <bits/stdc++.h>
using namespace std;
#define ll long long
char a[100100];
int main()
{
    int i,j,k,m,n,w,h;
    cin>>w>>h>>n;
    int x,y,a;
    int Map[110][110];
    memset(Map,0,sizeof(Map));
    for(i=1; i<=n; i++)
    {
        cin>>x>>y>>a;
        if(a==1)
        {
            for(j=0; j<x; j++)
            {
                for(k=0; k<=h; k++)
                    Map[j][k]=1;
            }
        }
        if(a==2)
        {
            for(j=x+1; j<=w; j++)
            {
                for(k=0; k<=h; k++)
                    Map[j][k]=1;
            }
        }
        if(a==3)
        {
            for(j=0; j<y; j++)
            {
                for(k=0; k<=w; k++)
                    Map[k][j]=1;
            }
        }
        if(a==4)
        {
            for(j=y+1; j<=h; j++)
            {
                for(k=0; k<=w; k++)
                    Map[k][j]=1;
            }
        }
    }
    int cnt=0;
    for(i=h; i>=0; i--)
    {
        for(j=0; j<=w; j++)
        {
            
            if(Map[j][i]==0)
                cnt++;
        }
        
    }

    if(cnt==0)
        cout<<0<<endl;
    else
        cout<<(sqrt(cnt)-1)*(sqrt(cnt)-1)<<endl;
    return 0;
}