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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.NoSuchElementException;

public final class Main {
	public static void main(String[] args) throws java.lang.Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] arg = br.readLine().split(" ");
		int w = Integer.parseInt(arg[0]);
		int h = Integer.parseInt(arg[1]);
		int n = Integer.parseInt(arg[2]);
		int wa[] = new int[n];
		int ha[] = new int[n];
		int aa[] = new int[n];
		for (int i = 0; i < n; i++) {
			arg = br.readLine().split(" ");
			wa[i] = Integer.parseInt(arg[0]);
			ha[i] = Integer.parseInt(arg[1]);
			aa[i] = Integer.parseInt(arg[2]);
		}

		Solver sol = new Solver();
		System.out.println(sol.solve(wa, ha, aa, w, h));
	}

}

class Solver {

	int solve(int[] wa, int[] ha, int[] aa, int w, int h) {

		int xLT = w, xGT = 0, yLT = h, yGT = 0;
		for (int i = 0; i < wa.length; i++) {
			int tempXLT = 0, tempXGT = 0, tempYLT = 0, tempYGT = 0;
			if (aa[i] == 1) {
				tempXGT = wa[i];
				if (xGT < tempXGT)
					xGT = tempXGT;

			} else if (aa[i] == 2) {
				tempXLT = wa[i];
				if (xLT > tempXLT)
					xLT = tempXLT;

			} else if (aa[i] == 3) {
				tempYGT = ha[i];
				if (yGT < tempYGT)
					yGT = tempYGT;
			} else if (aa[i] == 4) {
				tempYLT = ha[i];
				if (yLT > tempYLT)
					yLT = tempYLT;

			}
		}
		return xLT >= xGT && yLT >= yGT ? (xLT - xGT) * (yLT - yGT) : 0;

	}

}