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)

#![allow(dead_code)]
#![allow(unused_macros)]

// 入力マクロ
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

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

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

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

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

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

// #[allow(unused_imports)]
// use std::time::Instant;
// macro_rules! measure {
//     ( $x:expr) => {{
//         let start = Instant::now();
//         let result = $x;
//         let end = start.elapsed();
//         println!("Running in : {}.{:03}s", end.as_secs(), end.subsec_millis());
//         result
//     }};
// }

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
const MOD: u64 = 1_000_000_007;
fn main() {
    input! {
        w: usize, h: usize, n: usize,
        op: [(usize, usize, u8); n]
    }
    
    let mut board = vec![vec![false; w]; h];

    for (a, b, p) in op {
        match p {
            1 => {
                for l in board.iter_mut() {
                    for e in 0..a {
                        l[e] = true;
                    }
                }
            }
            2 => {
                for l in board.iter_mut() {
                    for e in a..w {
                        l[e] = true;
                    }
                }
            }
            3 => {
                for l in board.iter_mut().take(b) {
                    for e in l {
                        *e = true;
                    }
                }
            }
            4 => {
                for l in board.iter_mut().skip(b) {
                    for e in l {
                        *e = true;
                    }
                }
            }
            _ => { unreachable!() }
        }
    }

    // println!("{:?}", board);

    let ans: usize = board.iter().map(|i| i.iter().filter(|x| !**x).count()).sum();
    println!("{}", ans);
}


// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

/// プログラムを終了
fn exit() {
    use std::process;
    process::exit(0)
}

/// 比較可能な2つの引数のうち大きい方を返す
fn max<T: PartialOrd>(n: T, m: T) -> T {
    if n >= m {
        n
    } else {
        m
    }
}

/// 比較[可能な2つの引数のうち小さい方を返す
fn min<T: PartialOrd>(n: T, m: T) -> T {
    if n <= m {
        n
    } else {
        m
    }
}

/// floor + as i64
fn into_floor(a: f64) -> i64 {
    (a - a % 1.0) as i64
}

/// ceil + as i64
fn into_ceil(a: f64) -> i64 {
    (a - a % 1.0) as i64 + 1i64
}

/// "Yes", "No" を出力
fn yes_no(flag: bool) {
    if flag {
        println!("Yes");
    } else {
        println!("No");
    }
}

/// 互除法を用いて最大公約数を求める
fn gcd(n: u64, m: u64) -> u64 {
    let (mut n, mut m) = (max(n, m), min(n, m));
    if m == 0 {
        return n;
    }
    let mut _r = 0;
    while n % m != 0 {
        _r = n % m;
        n = m;
        m = _r;
    }
    m
}

/// 最小公倍数を求める
fn lcm(n: u64, m: u64) -> u64 {
    n * m / gcd(n, m)
}

/// 配列全体の最大公約数
fn gcd_vec(v: &[u64]) -> u64 {
    let mut r = v[0];
    for i in v.iter().skip(1) {
        r = gcd(r, *i);
    }
    r
}

/// 配列全体の最小公倍数
fn lcm_vec(v: &[u64]) -> u64 {
    let mut r = v[0];
    for i in v.iter().skip(1) {
        r = lcm(r, *i);
    }
    r
}

/// Find the first factor (other than 1) of a number
fn firstfac(x: u64) -> u64 {
    if x % 2 == 0 {
        return 2;
    };
    // TODO: return to step_by
    // for n in (3..).step_by(2).take_while(|m| m*m <= x) {
    for n in (1..).map(|m| 2 * m + 1).take_while(|m| m * m <= x) {
        if x % n == 0 {
            return n;
        };
    }
    // No factor found. It must be prime.
    x
}

/// Test whether a number is prime. Checks every odd number up to `sqrt(n)`.
fn is_prime(n: u64) -> bool {
    if n <= 1 {
        return false;
    }
    firstfac(n) == n
}

// TODO!
// pub fn parmutation<T: PartialOrd>(v: &Vec<T>) -> Vec<Vec<T>> {
//     let mut sorted = v;

// }