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)

// Template from https://techracho.bpsinc.jp/jhonda/2019_08_05/78537

// input macro for competive-programming from https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, bytes) => {
        read_value!($iter, String).into_bytes()
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

fn main() {
    use std::io::Read;
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();

    println!("{}", solve(&s));
}

macro_rules! test {
    ($($input:expr => $output:expr),* $(,)*) => {
        #[test]
        fn solve_test() {
            $(
                assert_eq!(solve($input), $output);
            )*
        }
    };
}

test! {
r#"5 4 2
2 1 1
3 3 4"# => r#"9"#,

r#"5 4 3
2 1 1
3 3 4
1 4 2"# => r#"0"#,

r#"10 10 5
1 6 1
4 1 3
6 9 4
9 4 2
3 1 3"# => r#"64"#,
}

// a = 1: x <= xi
// a = 2: x > xi
// a = 3: y <= yi
// a = 4: y > yi

fn solve(src: &str) -> String {
    input! {
        source = src,
        w: usize, h: usize, n: usize,
        xya: [(usize, usize, usize); n],
    }
    let mut q = vec![vec![false; w]; h];

    // // デバッグコード
    // q[1][2] = true;
    // q[2][2] = true;
    // q[3][3] = true;
    // for i in (0..h).rev() {
    //     let s:Vec<String> = q[i].iter().map(|&j| if j { "o" } else { "x" }.to_string()).collect();
    //     println!("{:?}", s.join(""));
    // }
    // println!("---------------");

    for y in 0..h {
        for x in 0..w {
            for i in 0..n {
                if (xya[i].2 == 1 && x < xya[i].0) || (xya[i].2 == 2 && x >= xya[i].0) || (xya[i].2 == 3 && y < xya[i].1) || (xya[i].2 == 4 && y >= xya[i].1) {
                    q[y][x] = true;
                }
            }
        }
    }

    // // デバッグコード
    // for i in (0..h).rev() {
    //     let s:Vec<String> = q[i].iter().map(|&j| if j { "o" } else { "x" }.to_string()).collect();
    //     println!("{:?}", s.join(""));
    // }
    // println!("---------------");

    // // デバッグコード
    // let s:Vec<usize> = q.iter().map(|qx| qx.iter().filter(|&&n| n).count()).collect();
    // println!("{:?}", s);
    // println!("\n---------------");

    q.iter().map(|qx| qx.iter().filter(|&&n| !n).count()).sum::<usize>().to_string()
}