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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        Main m = new Main(sc);
        m.show(m.solve());
        sc.close();
    }
    
	//フィールド
    Scanner sc;
    int W;
    int H;
    int N;
    int[] x;
    int[] y;
    int[] a;
    
    //入力
    Main(Scanner sc) {
        this.sc = sc;
        this.W = sc.nextInt();
        this.H = sc.nextInt();
        this.N = sc.nextInt();
        x = new int[N];
        y = new int[N];
        a = new int[N];
        for (int i=0; i<N; i++) {
        	x[i] = sc.nextInt();
        	y[i] = sc.nextInt();
        	a[i] = sc.nextInt();
        }
    }
    
    //解答処理
    private int solve() {
        int answer = 0;
        
        int lx = 0; //長方形左下のx座標
        int ly = 0; //長方形左下のy座標
        int rx = W; //長方形右上のx座標
        int ry = H; //長方形右上のy座標
        //右下と左上は(W,0)、(0,H)
        
        for(int i=0; i<N; i++){
          if(a[i] == 1){ //x[i]>xの領域を塗りつぶす
            lx = Math.max(lx, x[i]);
          }else if(a[i] == 2){ //x[i]<xの領域を塗りつぶす
            rx = Math.min(rx, x[i]);
          }else if(a[i] == 3){ //y[i]>yの領域を塗りつぶす
            ly = Math.max(ly, y[i]);
          }else if(a[i] == 4){ //y[i]<yの領域を塗りつぶす
            ry = Math.min(ry, y[i]);
          }
        }
        
        answer = (rx-lx) * (ry-ly);
        if ((rx-lx) < 0 || (ry-ly) < 0) {
        	answer = 0;
        }
        return answer;
    }
    
    //出力
    public void show(int answer) {
        System.out.println(answer);
    }

}