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)

use std::io::{stdin, Read, StdinLock};
use std::str::FromStr;

#[allow(dead_code)]
struct Scanner<'a> {
    cin: StdinLock<'a>,
}
#[allow(dead_code)]
impl<'a> Scanner<'a> {
    fn new(cin: StdinLock<'a>) -> Scanner<'a> {
        Scanner { cin: cin }
    }

    fn read<T: FromStr>(&mut self) -> Option<T> {
        let token = self.cin.by_ref().bytes().map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect::<String>();
        token.parse::<T>().ok()
    }

    fn input<T: FromStr>(&mut self) -> T {
        self.read().unwrap()
    }
}

fn main() {
    let cin = stdin();
    let cin = cin.lock();
    let mut sc = Scanner::new(cin);

    let (w, h, n): (i64, i64, i64) = (sc.input(), sc.input(), sc.input());
    let points: Vec<(i64, i64, i64)> = (0..n)
        .map(|_| (sc.input(), sc.input(), sc.input()) )
        .collect();

    let mut rectangle = vec![vec![0; w as usize]; h as usize];

    for (x, y, a)  in points {
        let x = x - 1;
        let y = y - 1;

        if a == 1 {
            for ix in 0..x + 1 {
                for y in 0..h {
                    rectangle[y as usize][ix as usize] = 1;
                }
            }
        } else if a == 2 {
            for ix in x + 1..w {
                for y in 0..h {
                    rectangle[y as usize][ix as usize] = 1;
                }
            }
        } else if a == 3 {
            for iy in 0..y + 1 {
                for x in 0..w {
                    rectangle[iy as usize][x as usize] = 1;
                }
            }
        } else if a == 4 {
            for iy in y + 1..h {
                for x in 0..w {
                    rectangle[iy as usize][x as usize] = 1;
                }
            }
        }

    }

    let mut ans = 0;
    for i in 0..h as usize {
        for j in 0..w as usize {
            if rectangle[i][j] == 0 {
                ans += 1;
            }
        }
    }
    println!("{}", ans);
}