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 (1.42.0) (judge verdict: Accepted)

#[allow(dead_code)]
fn main() {
    let stdin = stdin();
    let mut reader = StdinReader::new(stdin.lock());
    let (w, h, n) = reader.u3();
    let xya = reader.uv3(n);

    let mut left = 0;
    let mut right = w;
    let mut up = h;
    let mut down = 0;
    for (x, y, a) in xya {
        match a {
            1 => left = max(x, left),
            2 => right = min(x, right),
            3 => down = max(y, down),
            4 => up = min(y, up),
            _ => unreachable!(),
        }
    }

    //dbg!(&right, &left, &down, &up);
    if left >= right || down >= up {
        println!("{}", 0);
        return;
    }
    println!("{}", (right - left) * (up - down));
}

#[allow(unused_imports)]
use itertools::Itertools;
#[allow(unused_imports)]
use std::{cmp::*, collections::*, io::*, num::*, str::*};
#[allow(unused_imports)]
use stdin_reader::StdinReader;

#[allow(dead_code)]
mod stdin_reader {
    use std::fmt::Debug;
    use std::io::*;
    use std::str::*;

    pub struct StdinReader<R: BufRead> {
        reader: R,
        buf: Vec<u8>,
        // Should never be empty
        pos: usize, // Should never be out of bounds as long as the input ends with '\n'
    }

    impl<R: BufRead> StdinReader<R> {
        pub fn new(r: R) -> StdinReader<R> {
            StdinReader {
                reader: r,
                buf: Vec::new(),
                pos: 0,
            }
        }
        pub fn next<T: FromStr>(&mut self) -> T
        where
            T::Err: Debug,
        {
            if self.buf.is_empty() {
                self._read_next_line();
            }
            let mut start = None;
            loop {
                if self.pos == self.buf.len() {
                    break;
                }
                match (self.buf[self.pos], start.is_some()) {
                    (b' ', true) | (b'\n', true) => break,
                    (_, true) | (b' ', false) => self.pos += 1,
                    (b'\n', false) => self._read_next_line(),
                    (_, false) => start = Some(self.pos),
                }
            }
            let target = &self.buf[start.unwrap()..self.pos];
            from_utf8(target).unwrap().parse().unwrap()
        }

        fn _read_next_line(&mut self) {
            self.pos = 0;
            self.buf.clear();
            if self.reader.read_until(b'\n', &mut self.buf).unwrap() == 0 {
                panic!("Reached EOF");
            }
        }

        pub fn str(&mut self) -> String {
            self.next()
        }
        pub fn s(&mut self) -> Vec<char> {
            self.next::<String>().chars().collect()
        }
        pub fn i(&mut self) -> i64 {
            self.next()
        }
        pub fn i2(&mut self) -> (i64, i64) {
            (self.next(), self.next())
        }
        pub fn i3(&mut self) -> (i64, i64, i64) {
            (self.next(), self.next(), self.next())
        }
        pub fn u(&mut self) -> usize {
            self.next()
        }
        pub fn u2(&mut self) -> (usize, usize) {
            (self.next(), self.next())
        }
        pub fn u3(&mut self) -> (usize, usize, usize) {
            (self.next(), self.next(), self.next())
        }
        pub fn u4(&mut self) -> (usize, usize, usize, usize) {
            (self.next(), self.next(), self.next(), self.next())
        }
        pub fn u5(&mut self) -> (usize, usize, usize, usize, usize) {
            (
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
            )
        }
        pub fn u6(&mut self) -> (usize, usize, usize, usize, usize, usize) {
            (
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
                self.next(),
            )
        }
        pub fn f(&mut self) -> f64 {
            self.next()
        }
        pub fn f2(&mut self) -> (f64, f64) {
            (self.next(), self.next())
        }
        pub fn c(&mut self) -> char {
            self.next::<String>().pop().unwrap()
        }
        pub fn iv(&mut self, n: usize) -> Vec<i64> {
            (0..n).map(|_| self.i()).collect()
        }
        pub fn iv2(&mut self, n: usize) -> Vec<(i64, i64)> {
            (0..n).map(|_| self.i2()).collect()
        }
        pub fn iv3(&mut self, n: usize) -> Vec<(i64, i64, i64)> {
            (0..n).map(|_| self.i3()).collect()
        }
        pub fn uv(&mut self, n: usize) -> Vec<usize> {
            (0..n).map(|_| self.u()).collect()
        }
        pub fn uv2(&mut self, n: usize) -> Vec<(usize, usize)> {
            (0..n).map(|_| self.u2()).collect()
        }
        pub fn uv3(&mut self, n: usize) -> Vec<(usize, usize, usize)> {
            (0..n).map(|_| self.u3()).collect()
        }
        pub fn uv4(&mut self, n: usize) -> Vec<(usize, usize, usize, usize)> {
            (0..n).map(|_| self.u4()).collect()
        }
        pub fn fv(&mut self, n: usize) -> Vec<f64> {
            (0..n).map(|_| self.f()).collect()
        }
        pub fn cmap(&mut self, h: usize) -> Vec<Vec<char>> {
            (0..h).map(|_| self.s()).collect()
        }
    }
}