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;
using static Atcoder;
using System.Threading.Tasks;
using System.ComponentModel;

public class Hello
{

    public static void Main()
    {
        int[] num = SpRead(' ').Select(a => int.Parse(a)).ToArray();
        int x = num[0];
        int y = num[1];
        int[] n = new int[3];
        bool[,] log = new bool[x, y];
        for (int i = 0; i < num[2]; i++)
        {
            n = SpRead(' ').Select(a => int.Parse(a)).ToArray();
            if (n[2] == 1)
            {
                for (int j = 0; j < n[0]; j++)
                {
                    for (int k = 0; k < y; k++)
                    {
                        log[j, k] = true;
                    }
                }
            }
            else if (n[2] == 2)
            {
                for (int j = n[0]; j < x; j++)
                {
                    for (int k = 0; k < y; k++) log[j, k] = true;
                }
            }
            else if (n[2] == 3)
            {
                for (int j = 0; j < n[1]; j++)
                {
                    for (int k = 0; k < x; k++) log[k, j] = true;
                }
            }
            else if (n[2] == 4)
            {
                for (int j = n[1]; j < y; j++)
                {
                    for (int k = 0; k < x; k++)
                    {
                        log[k, j] = true;
                    }
                }
            }

        }
        int count = 0;
        for (int i = 0; i < x; i++)
        {
            for (int j = 0; j < y; j++)
            {
                if (log[i, j]) count++;
            }
        }
        Console.WriteLine(x*y-count);
    }
}



public class Atcoder
{
    static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
    public static int LCM(int a, int b)
    {
        int c = a * b;
        if (a < b) Swap(ref a, ref b);
        int d = a % b;
        while (d != 0)
        {
            a = b;
            b = d;
            d = a % b;
        }
        return c / b;
    }
    public static string strReverce(string s)
    {
        return new string(s.Reverse().ToArray());
    }
    public static int Cin()
    {
        return int.Parse(Console.ReadLine());
    }
    public static bool IsPrime(int n)
    {
        if (n < 2) return false;
        if (n == 2) return true;
        if (n % 2 == 0) return false;

        //double sqrtNum = Math.Sqrt(n);
        for (int i = 3; i < n; i += 2)
        {
            if (n % i == 0) return false;
        }
        return true;
    }
    public static string[] SpRead(char c)
    {
        return Console.ReadLine().Split(c);
    }
}