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)

#[allow(unused_imports)]
use std::char::*;
#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::*;
use std::str::FromStr;

#[allow(unused_macros)]
macro_rules! debug {($($a:expr),*) => {println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);}}
#[allow(unused_macros)]
macro_rules! input {(source=$s:expr,$($r:tt)*) => {let mut iter=$s.split_whitespace(); let mut next=||{iter.next().unwrap()}; input_inner! {next,$($r)*}};($($r:tt)*) => {let stdin=std::io::stdin();let mut bytes=std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next=move||->String{bytes.by_ref().map(|r|r.unwrap() as char).skip_while(|c|c.is_whitespace()).take_while(|c|!c.is_whitespace()).collect()}; input_inner! {next,$($r)*}};}
#[allow(unused_macros)]
macro_rules! input_inner {($next:expr) => {}; ($next:expr,) => {}; ($next:expr,$var:ident:$t:tt$($r:tt)*) => {let $var=read_value!($next,$t); input_inner! {$next$($r)*}};}
#[allow(unused_macros)]
macro_rules! read_value {($next:expr,($($t:tt),*)) => {($(read_value! ($next,$t)),*)}; ($next:expr, [$t:tt; $len:expr]) => {(0..$len).map(|_|read_value! ($next,$t)).collect::<Vec<_>>()}; ($next:expr,chars) => {read_value! ($next,String).chars().collect::<Vec<char>>()}; ($next:expr,usize1) => {read_value! ($next,usize)-1}; ($next:expr,$t:ty) => {$next().parse::<$t>().expect("Parse error")};}

#[derive(PartialEq, PartialOrd)]
pub struct Total<T>(pub T);
impl<T: PartialEq> Eq for Total<T> {}
impl<T: PartialOrd> Ord for Total<T> {
    fn cmp(&self, other: &Total<T>) -> std::cmp::Ordering {
        self.0.partial_cmp(&other.0).unwrap()
    }
}

#[allow(dead_code)]
const MAX: usize = 100006;
#[allow(dead_code)]
const INF_U32: u32 = 1 << 31;
#[allow(dead_code)]
const INF_I32: i32 = 1 << 30;
#[allow(dead_code)]
const INF_U64: u64 = 1 << 63;
#[allow(dead_code)]
const INF_I64: i64 = 1 << 62;
#[allow(dead_code)]
const MOD: i64 = 1e9 as i64 + 7;

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

#[allow(unused_imports)]
use std::f64;


fn main() {
    input!{w:i64, h:i64, n:usize, p:[(i64,i64,i64);n]};
    let mut w = w;
    let mut h = h;
    let mut w0 = 0i64;
    let mut h0 = 0i64;
    for i in 0..n {
        let (x,y,a) = p[i];
        if a == 1 {
            w0 = max(w0,x);
        }
        else if a == 2 {
            w = min(w,x);
        }
        else if a == 4 {
            h = min(h,y);
        }
        else if a == 3 {
            h0 = max(h0,y);
        }
        //debug!(w0,h0,w,h);
    }

    if w <= w0 || h <= h0 {
        println!("0");
    }
    else {
        println!("{}", (w-w0)*(h-h0));
    }

}