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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function myout(text){console.log(text);}//standard output
function Main(input) {
	//input = parseInt(input);
	//input = input.trim().split(" ");
	input = input.trim().split("\n");
	//input = input.trim().split(" ").map((a)=>Number(a));
	//input = input.trim().split("\n").map((a)=>Number(a));
  var Wmax = parseInt(input[0].split(" ")[0]);
  var Hmax = parseInt(input[0].split(" ")[1]);
  var N = parseInt(input[0].split(" ")[2]);
  var Wmin = 0;
  var Hmin = 0;
  for(var i = 1; i <= N ; i++){
    var tmp = input[i].split(" ").map((a)=>Number(a));
    switch(tmp[2]){
      case 1:
        Wmin = tmp[0];
        break;
      case 2:
        Wmax = tmp[0];
        break;
      case 3:
        Hmin = tmp[1];
        break;
      case 4:
        Hmax = tmp[1];
        break;
    }
  }
  if(Wmin > Wmax || Hmin > Hmax){
     myout("0");
  }else{
    myout((Wmax - Wmin) * (Hmax - Hmin));
  }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());