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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.ComponentModel.DataAnnotations;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] WHN = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
            long W = WHN[0];
            long H = WHN[1];
            long N = WHN[2];
            Boolean[,] color = new Boolean[W, H];

            for (int j = 0; j < N; j++)
            {
                long[] xya = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();
                long x = xya[0];
                long y = xya[1];
                long z = xya[2];
                if (z == 1)
                {
                    //xの左側
                    for (int f = (int)x; 0 < f; f--)
                    {
                        for (int k = 0; k < H; k++)
                        {
                            color[f - 1, k] = true;
                        }
                    }
                }
                else if (z == 2)
                {
                    //xの右側
                    for (int f = (int)x; f < W; f++)
                    {
                        for (int k = 0; k < H; k++)
                        {
                            color[f, k] = true;
                        }
                    }
                }
                else if (z == 3)
                {
                    try
                    {
                        //yの下
                        for (int k = (int)y; 0 < k; k--)
                        {
                            for (int f = 0; f < H; f++)
                            {
                                color[f, k - 1] = true;
                            }
                        }
                    }
                    catch
                    {
                        color[1, 0] = true;
                    }
                }
                else if (z == 4)
                {
                    //yの上
                    for (int k = (int)y; k < H; k++)
                    {
                        for (int f = 0; f < W; f++)
                        {
                            color[f, k] = true;
                        }
                    }
                }
            }
            int cnt = 0;
            for(int f = 0; f < W; f++)
            {
                for(int k = 0; k < H; k++)
                {
                    if (!color[f, k])
                    {
                        cnt++;
                    }
                }
            }
            Console.WriteLine(cnt);
        }
    }
}
// 文字列の入力
//string s = Console.ReadLine();

// 整数の入力
//long n = long.Parse(Console.ReadLine());

// 文字列配列の入力
//string[] inputStrArray = Console.ReadLine().Split(' ');

// 整数配列の入力
//long[] inputLongArray = Console.ReadLine().Split(' ').Select(i => long.Parse(i)).ToArray();


//Console.WriteLine(ans);