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 12.16.1) (judge verdict: Accepted)

// https://atcoder.jp/contests/abc047/tasks/abc047_b
"use strict";
function Main(input) {
  const [basePoint, ...points] = input.trim().split("\n");
  const [W, H, N] = basePoint.trim().split(" ").map(Number);
  const field = Array(W)
    .fill()
    .map(() => Array(H).fill(1));

  for (let i = 0; i < N; i++) {
    const [x, y, a] = points[i].trim().split(" ").map(Number);

    let [jmin, jmax, kmin, kmax] = [0, 0, 0, 0];
    if (a === 1) {
      [jmin, jmax, kmin, kmax] = [0, x, 0, H];
    } else if (a === 2) {
      [jmin, jmax, kmin, kmax] = [x, W, 0, H];
    } else if (a === 3) {
      [jmin, jmax, kmin, kmax] = [0, W, 0, y];
    } else if (a === 4) {
      [jmin, jmax, kmin, kmax] = [0, W, y, H];
    }

    for (let j = jmin; j < jmax; j++) {
      for (let k = kmin; k < kmax; k++) {
        field[j][k] = 0;
      }
    }
  }

  const area = field.flat().reduce((acc, cur) => acc + cur, 0);
  console.log(area);
}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));