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 (1.15.1) (judge verdict: Accepted)

fn read_spc<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}

fn main() {
    snuke();
}

fn snuke() {
    let whn: Vec<i64> = read_spc();
    let mut w = whn[0];
    let w0 = whn[0];
    let mut h = whn[1];
    let h0 = whn[1];
    let n = whn[2];
    let mut xya: Vec<Vec<i64>> = vec![];
    for i in 0..n {
        let xya_i: Vec<i64> = read_spc();
        xya.push(xya_i);
    }
    let mut x1 = 0;
    let mut x2 = w;
    let mut y3 = 0;
    let mut y4 = h;
    for xya_i in xya {
        let x = xya_i[0];
        let y = xya_i[1];
        let a = xya_i[2];
        match a {
            1 => x1 = max_i64(x1, x),
            2 => x2 = min_i64(x2, x),
            3 => y3 = max_i64(y3, y),
            _ => y4 = min_i64(y4, y)
        }
    }
    w = max_i64(0, x2 - x1);
    h = max_i64(0, y4 - y3);
    println!("{}", w * h);
}

fn max_i64(n: i64, m: i64) -> i64 {
    let diff = n - m;
    match diff {
        diff if diff < 0 => m,
        _                => n
    }
}

fn min_i64(n: i64, m: i64) -> i64 {
    let diff = n - m;
    match diff {
        diff if diff > 0 => m,
        _                => n
    }
}