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-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using static System.Console;

namespace atcorder2
{
    class Program
    {
        public static long Read()
        {
            return long.Parse(ReadLine());
        }

        public static long[] Reads()
        {
            return ReadLine().Split().Select(long.Parse).ToArray();
        }

        
         public static long gcd(long x, long y)
        {
            if (x < y) gcd(y, x);
            while (y != 0)
            {
                var z = x;
                x = y;
                y = z % y;
            }
            return x;
        }

        public static long C(long n, long k)
        {
            long x = 1;
            for (long i = 1; i <= k; i++)
            {
                x *= n - i + 1;
                x /= i;
            }
            return x;
        }
        static void Main(string[] args)
        {
            var sw = new StreamWriter(OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var q = Reads();
            var w = q[0];
            var h = q[1];
            var n = q[2];
            long left = 0;
            long right = w;
            long up = h;
            long down = 0;
            for (int i = 0; i < n; i++)
            {
                q = Reads();
                if (q[2] == 1) left = Math.Max(left,q[0]);
                if (q[2] == 2) right = Math.Min(right,q[0]);
                if (q[2] == 3) down = Math.Max(down,q[1]);
                if (q[2] == 4) up = Math.Min(up,q[1]);
            }

            if (left < right && down < up)
                WriteLine((right - left) * (up - down));
            else
                WriteLine(0);
            


            Console.Out.Flush();
        }
    }
}