Problem:
Score : 700 points

Problem Statement

Snuke is playing a puzzle game.
In this game, you are given a rectangular board of dimensions R × C, filled with numbers. Each integer i from 1 through N is written twice, at the coordinates (x_{i,1},y_{i,1}) and (x_{i,2},y_{i,2}).

The objective is to draw a curve connecting the pair of points where the same integer is written, for every integer from 1 through N.
Here, the curves may not go outside the board or cross each other.

Determine whether this is possible.

Constraints

1 ≤ R,C ≤ 10^8

1 ≤ N ≤ 10^5

0 ≤ x_{i,1},x_{i,2} ≤ R(1 ≤ i ≤ N)

0 ≤ y_{i,1},y_{i,2} ≤ C(1 ≤ i ≤ N)

All given points are distinct.

All input values are integers.

Input

Input is given from Standard Input in the following format:

R C N
x_{1,1} y_{1,1} x_{1,2} y_{1,2}
:
x_{N,1} y_{N,1} x_{N,2} y_{N,2}

Output

Print YES if the objective is achievable; print NO otherwise.

Sample Input 1

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2

Sample Output 1

YES

The above figure shows a possible solution.

Sample Input 2

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1

Sample Output 2

NO

Sample Input 3

5 5 7
0 0 2 4
2 3 4 5
3 5 5 2
5 5 5 4
0 3 5 1
2 2 4 4
0 5 4 1

Sample Output 3

YES

Sample Input 4

1 1 2
0 0 1 1
1 0 0 1

Sample Output 4

NO

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn to_index(x: i64, y: i64, r: i64, c: i64) -> i64 {
    if x == 0 {
        return y;
    } else if y == c {
        return c + x;
    } else if x == r {
        return c + r + (c - y);
    } else if y == 0 {
        return c + r + c + (r - x);
    }
    unreachable!();
}

fn main() {
    let v = read_vec::<i64>();
    let (r, c, n) = (v[0], v[1], v[2] as usize);
    let mut pairs = vec![];
    for i in 0..n {
        let v = read_vec::<i64>();
        let (x1, y1, x2, y2) = (v[0], v[1], v[2], v[3]);
        if (x1 == 0 || x1 == r || y1 == 0 || y1 == c) && (x2 == 0 || x2 == r || y2 == 0 || y2 == c)
        {
            pairs.push((x1, y1, x2, y2));
        }
    }

    let mut indexes = vec![];
    for (i, (x1, y1, x2, y2)) in pairs.into_iter().enumerate() {
        indexes.push((to_index(x1, y1, r, c), i));
        indexes.push((to_index(x2, y2, r, c), i));
    }
    indexes.sort();
    for i in 0..indexes.len() / 2 {
        let (_, idx1) = indexes[i];
        let (_, idx2) = indexes[indexes.len() - 1 - i];
        if idx1 != idx2 {
            println!("NO");
            return;
        }
    }
    println!("YES");
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}