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::env;
use std::io::prelude::*;
use std::io;
use std::fs::File;
use std::str::FromStr;
use std::io::BufReader;
fn buf_read() -> io::Result<(Vec<String>)> {
    let args: Vec<_> = env::args().collect();
    if args.len() >= 2 {
        let f = try!(File::open("input.txt"));
        let input_lines: Vec<_> = BufReader::new(f).lines().collect();
        let lines: Vec<String> = input_lines.into_iter().map(|e| e.unwrap()).collect();
        Ok((lines))
    } else {
        let stdin = io::stdin();
        let input_lines: Vec<_> = stdin.lock().lines().collect();
        let lines: Vec<String> = input_lines.into_iter().map(|e| e.unwrap()).collect();
        Ok((lines))
    }
}

fn main() {
    type Element = usize;
    let input = buf_read().unwrap();
    let mut input_vectors: Vec<Vec<Element>> = vec![];
    for input_line in input {
        let input_str: Vec<String> = input_line.split(' ').map(String::from).collect();
        let mut input_vector: Vec<Element> = vec![];
        for input_elem_str in input_str {
            let elem: Element = Element::from_str(input_elem_str.as_str()).unwrap();
            input_vector.push(elem);
        }
        input_vectors.push(input_vector);
    }
    let x_len = input_vectors[0][0];
    let y_len = input_vectors[0][1];
    let mut area: Vec<Vec<Element>> = vec![vec![0; x_len]; y_len];
    for i in 1..input_vectors[0][2] + 1 {
        match input_vectors[i][2] {
            1 => {
                for y in 0..y_len {
                    for x in 0..input_vectors[i][0] {
                        area[y][x] = 1;
                    }
                }
            }
            2 => {
                for y in 0..y_len {
                    for x in input_vectors[i][0]..x_len {
                        area[y][x] = 1;
                    }
                }
            }
            3 => {
                for x in 0..x_len {
                    for y in 0..input_vectors[i][1] {
                        area[y][x] = 1;
                    }
                }
            }
            _ => {
                for x in 0..x_len {
                    for y in input_vectors[i][1]..y_len {
                        area[y][x] = 1;
                    }
                }
            }
        }
    }
    let black_sum: usize = area.iter()
                               .fold(0, |acc, ref x| acc + x.iter().fold(0, |sum, acc| sum + acc));
    println!{"{:?}", x_len * y_len - black_sum}
}