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;

fn procon_read<T: std::str::FromStr>() ->  Vec<T> {
	let mut buf = String::new();
	io::stdin().read_line(&mut buf).expect("");
	let iter = buf.split_whitespace();
	let mut v: Vec<T> = Vec::new();
	for i in iter {
		v.push(i.parse().ok().unwrap());
	}
	v
}

fn main() {
	let v:Vec<i32> = procon_read();
	let w = v[0];
	let h = v[1];
	let n = v[2];
	let mut x:Vec<i32> = Vec::new();
	let mut y:Vec<i32> = Vec::new();
	let mut a:Vec<i32> = Vec::new();
	for i in 0..n {
		let v:Vec<i32> = procon_read();
		x.push(v[0]);
		y.push(v[1]);
		a.push(v[2]);
	}
	let mut leftx = 0;
	let mut lefty = 0;
	let mut rightx = w;
	let mut righty = h;
	for i in 0..n {
		if a[i as usize] == 1 {
			if leftx < x[i as usize] {
				leftx = x[i as usize];
			}
		}else if a[i as usize] == 2 {
			if rightx > x[i as usize] {
				rightx = x[i as usize];
			}
		}else if a[i as usize] == 3 {
			if lefty < y[i as usize] {
				lefty = y[i as usize];
			}
		}else{
			if righty > y[i as usize] {
				righty = y[i as usize];
			}
		}
	}
	if (righty - lefty) < 0 || (rightx - leftx) < 0{
		println!("0");
	}else{
		println!("{}", (righty - lefty)*(rightx -leftx));
	}
}