Problem: 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.

Examples

Input

5 4 2
2 1 1
3 3 4


Output

9


Input

5 4 3
2 1 1
3 3 4
1 4 2


Output

0


Input

10 10 5
1 6 1
4 1 3
6 9 4
9 4 2
3 1 3


Output

64

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		
		//変数//
		int W;		//右上頂点x座標
		int H;		//右上頂点y座標
		int N;		//長方形内の点の個数
		int minwx;	//白い部分のx座標始まり
		int maxwx;	//白い部分のx座標終わり
		int minwy;	//白い部分のy座標始まり
		int maxwy;	//白い部分のy座標終わり
		int warea;	//白い部分の面積
		
		int[] x;	//点のｘ座標
		int[] y;	//点のy座標
		int[] a;	//指定範囲ルールナンバー
		
		Scanner scan = new Scanner(System.in);
		
		//入力//
		W = scan.nextInt();
		H = scan.nextInt();
		N = scan.nextInt();
		
		x = new int[N];
		y = new int[N];
		a = new int[N];
		
		for(int i = 0; i < N; i++){
			x[i] = scan.nextInt();
			y[i] = scan.nextInt();
			a[i] = scan.nextInt();
		}
		
		scan.close();
		
		//処理//
		//初期処理
		minwx = 0;
		maxwx = W;
		minwy = 0;
		maxwy = H;
		
		//ルールナンバーごとに処理
		for(int j = 0; j < N; j++){
			if( a[j] == 1 && minwx < x[j] ){
				minwx = x[j];
			}else if( a[j] == 2 && maxwx > x[j] ){
				maxwx = x[j];
			}else if( a[j] == 3 && minwy < y[j] ){
				minwy = y[j];
			}else if( a[j] == 4 && maxwy > y[j] ){
				maxwy = y[j];
			}
		}
		
		//白い部分が残っているかどうか判定
		if( minwx >= maxwx || minwy >= maxwy ){
			warea = 0;
		}else{
			warea = (maxwx - minwx) * (maxwy - minwy);
		}
		
		//結果//
		System.out.println(warea);

	}

}