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: Accepted)

'use strict'

function main(s) {

  s = s.split('\n');

  const w = Number(s[0].split(' ')[0]);
  const h = Number(s[0].split(' ')[1]);

  const xyas = s.slice(1, -1).map(l => l.split(' ').map(n => Number(n)));

  const bucket = [...Array(h)].map(l => [...Array(w)].fill(0));

  for (const xya of xyas) {
    const x = xya[0];
    const y = xya[1];
    const a = xya[2] - 1;

    const fromH = [0, 0, 0, y];
    const toH   = [h, h, y, h];
    const fromW = [0, x, 0, 0];
    const toW   = [x, w, w, w];

    for (let i = fromH[a]; i < toH[a]; i++) {
      for (let j = fromW[a]; j < toW[a]; j++) {
        bucket[i][j] = 1;
      }
    }
  }

  let count = 0;
  for (let i = 0; i < h; i++) {
    for (let j = 0; j < w; j++) {
      if (bucket[i][j] === 0) count += 1;
    }
  }

  console.log(count);
}

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