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 Rust (1.42.0) (judge verdict: Accepted)

use whiteread::parse_line;

fn main() {
    let (w, h, n): (usize, usize, usize) = parse_line().unwrap();

    let mut is_white: Vec<Vec<bool>> = vec![];
    for _ in 0..w {
        let mut v = vec![];
        for _ in 0..h {
            v.push(true);
        }
        is_white.push(v);
    }
    for _ in 0..n {
        let (x, y, a): (usize, usize, usize) = parse_line().unwrap();
        let (x_range, y_range) = match a {
            1 => (0..x, 0..h),
            2 => (x..w, 0..h),
            3 => (0..w, 0..y),
            4 => (0..w, y..h),
            _ => unreachable!(),
        };

        for i in x_range {
            for j in y_range.clone() {
                is_white[i][j] = false;
            }
        }
    }

    let mut ret = 0;
    for i in 0..w {
        for j in 0..h {
            if is_white[i][j] {
                ret += 1;
            }
        }
    }

    println!("{}", ret);
}