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: Wrong Answer)

using System;
using System.Collections.Generic;

namespace Project
{
	class MainClass
	{
		public static void Main(string[] args)
		{
			string[] s = Console.ReadLine().Split(' ');
			int W, H, N;
			W = int.Parse(s[0]);
			H = int.Parse(s[1]);
			N = int.Parse(s[2]);
			int[] x = new int[N];
			int[] y = new int[N];
			int[] a = new int[N];
			for (int i = 0; i < N; i++)
			{
				string[] ss = Console.ReadLine().Split(' ');
				x[i] = int.Parse(ss[0]);
				y[i] = int.Parse(ss[1]);
				a[i] = int.Parse(ss[2]);
			}
			List<int> a1 = new List<int>();
			List<int> a2 = new List<int>();
			List<int> a3 = new List<int>();
			List<int> a4 = new List<int>();

			for (int i = 0; i < N; i++)
			{
				switch (a[i])
				{
					case 1:
						a1.Add(x[i]);
						break;
					case 2:
						a2.Add(x[i]);
						break;
					case 3:
						a3.Add(y[i]);
						break;
					case 4:
						a4.Add(y[i]);
						break;
				}
			}
			a1.Sort();
			a2.Sort();
			a3.Sort();
			a4.Sort();
			int tate = H, yoko = W;
			if (a1.Count * a2.Count == 0)
			{
				if (a1.Count == 0 && a2.Count == 0)
					yoko = W;
				else if (a1.Count == 0)
					yoko = a2[a2.Count - 1];
				else
					yoko = W - a1[0];
			}
			else
			{
				yoko = a2[a2.Count - 1] - a1[0];
			}

			if (a3.Count * a4.Count == 0)
			{
				if (a3.Count == 0 && a4.Count == 0)
					tate = H;
				else if (a3.Count == 0)
					tate = a4[a4.Count - 1];
				else
					tate = H - a3[0];
			}
			else
			{
				tate = a4[a4.Count - 1] - a3[0];
			}
			if (tate <= 0 || yoko <= 0)
				Console.WriteLine(0);
			else
				Console.WriteLine(tate * yoko);

		}
	}
}