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: Wrong Answer)

use scanner::Scanner;

fn main() {
    let mut sc = Scanner::new();
    let w: i32 = sc.read();
    let h: i32 = sc.read();
    let n: i32 = sc.read();
    let mut pos1 = (0, 0);
    let mut pos2 = (w, h);
    let xya: Vec<(i32, i32, i32)> = (0..n).map(|_| (sc.read(), sc.read(), sc.read())).collect();

    for (x, y, a) in xya {
        if a == 1 {
            pos1 = (x, pos1.1)
        } else if a == 2 {
            pos2 = (x, pos2.1);
        } else if a == 3 {
            pos1 = (pos1.0, y);
        } else if a == 4 {
            pos2 = (pos2.0, y);
        }
    }
    println!("{}", if pos2.0 > pos1.0 || pos2.1 > pos1.0 { (pos2.0 - pos1.0) * (pos2.1 - pos1.1) } else { 0 });
}

mod scanner {
    pub struct Scanner<'a> {
        s: String,
        words: ::std::str::SplitWhitespace<'a>,
    }

    impl<'a> Scanner<'a> {
        pub fn new() -> Scanner<'a> {
            let s = String::new();
            let words = unsafe { ::std::mem::transmute(s.split_whitespace()) };
            Scanner { s: s, words: words }
        }

        pub fn read<T: ::std::str::FromStr>(&mut self) -> T {
            match self.words.next() {
                Some(x) => x.parse().ok().unwrap(),
                None => {
                    self.load();
                    self.read()
                }
            }
        }

        fn load(&mut self) {
            self.s.clear();
            ::std::io::stdin().read_line(&mut self.s).unwrap();
            self.words = unsafe { ::std::mem::transmute(self.s.split_whitespace()) };
        }
    }
}