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)

macro_rules! read_line {
    () => {{
        let mut input = String::new();
        std::io::stdin().read_line(&mut input).unwrap();
        input
    }};
}

fn read_to_vec<T: std::str::FromStr>() -> Vec<T> {
    read_line!().split_whitespace()
        .map(|e| e.parse::<T>().ok().unwrap())
        .collect()
}

fn main() {
    let input: Vec<i32> = read_to_vec();
    let (w, h, n) = (input[0], input[1], input[2]);
    let mut input: Vec<Vec<i32>> = vec![Vec::new(); 4];
    let zero: i32 = 0;

    for _ in 0..n {
        let line: Vec<i32> = read_to_vec();
        
        match line[2] {
            a @ 1...4 => input[(a-1) as usize].push(line[(a/3) as usize]),
            _ => panic!(),
        }
    }

    let (bottom, top, left, right) =
        (input[0].iter().max().unwrap_or(&zero),
        input[1].iter().min().unwrap_or(&w),
        input[2].iter().max().unwrap_or(&zero),
        input[3].iter().min().unwrap_or(&h));

    println!("{}",
        std::cmp::max(0, top - bottom) *
        std::cmp::max(0, right - left));
}