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;
class Program
{
    static void Main(string[] args)
    {
        new Program().Solve();
    }

    Scanner sc = new Scanner();
    void Solve()
    {
        int w = sc.NextInt();
        int h = sc.NextInt();
        int n = sc.NextInt();
        int maxX = w;
        int minX = 0;
        int maxY = h;
        int minY = 0;
        for (int i = 0; i < n; i++)
        {
            int x = sc.NextInt();
            int y = sc.NextInt();
            int a = sc.NextInt();
            if (a == 1) minX = Math.Max(minX, x);
            else if (a == 2) maxX = Math.Min(maxX, x);
            else if (a == 3) minY = Math.Max(minY, y);
            else if (a == 4) maxY = Math.Min(maxY, y);
        }
        int ans = (maxX - minX) * (maxY - minY);
        if (maxX - minX <= 0) ans = 0;
        if (maxY - minY <= 0) ans = 0;
        wl(ans);
        rk();
    }
    void SolveC()
    {
        int N = sc.NextInt();
        int T = sc.NextInt();
        int[] A = new int[N];
        for (int i = 0; i < N; i++) A[i] = sc.NextInt();
        int maxDiff = 0;
        int minV = A[0];
        int ans = 0;
        for (int i = 1; i < N; i++)
        {
            if (maxDiff < A[i] - minV)
            {
                maxDiff = A[i] - minV;
                ans = 0;
            }
            if (maxDiff == A[i] - minV)
            {
                ans++;
            }
            minV = min(minV, A[i]);
        }
        wl(ans);
        rk();
    }
    // ------------------------------------- //
    void wl(string v) { Console.WriteLine(v); }
    void wl(int v) { Console.WriteLine(v); }
    void rk() { Console.ReadKey(); }
    int max(int v1, int v2) { return Math.Max(v1, v2); }
    int min(int v1, int v2) { return Math.Min(v1, v2); }
    long gcd(long a, long b) { return b == 0 ? a : gcd(b, a % b); }
    long lcm(long a, long b) { return a / gcd(a, b) * b; }
}
class Scanner
{
    public Scanner() { }
    private string[] buff = null;
    private int bIndex = 0;
    public string Next()
    {
        if (buff == null || bIndex >= buff.Length)
        {
            buff = Console.ReadLine().Split(' ');
            bIndex = 0;
        }
        return buff[bIndex++];
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
}
class Pair<T, K>
{
    public Pair() { }
    public Pair(T f, K s)
    {
        first = f;
        second = s;
    }
    public T first {get; set;}
    public K second {get; set;}
}