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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

class Magatro
{
    static int W,H,N;
    static int[] x, y, a;
    static void Main()
    {
        Read();
        int ans;
        int ue = H, sita = 0, migi = W, hidari = 0;
       for(int i = 0; i < N; i++)
        {
            switch (a[i])
            {
                case 1:
                    hidari = Math.Max(hidari, x[i]);
                    break;
                case 2:
                    migi = Math.Min(migi, x[i]);
                    break;
                case 3:
                    sita = Math.Max(sita, y[i]);
                    break;
                case 4:
                    ue = Math.Min(ue, y[i]);
                    break;
            }
        }
        if (sita >= ue||migi<=hidari)
        {
            Console.WriteLine(0);
            return;
        }
        ans = (ue - sita) * (migi - hidari);
        Console.WriteLine(ans);
    }
    static void Read()
    {
        int[] q = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
        
        W = q[0];
        H = q[1];
        N = q[2];
        x = new int[N];
        y = new int[N];
        a = new int[N];
        for(int i = 0; i < N; i++)
        {
            q = Console.ReadLine().Split(' ').Select(s => int.Parse(s)).ToArray();
            x[i] = q[0];
            y[i] = q[1];
            a[i] = q[2];
        }
    }
}