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: Accepted)

use std::io::*;
use std::str::FromStr;

#[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")
}

fn main() {
    let w = read::<i32>();
    let h = read::<i32>();
    let n = read::<usize>();
    let mut ps = vec![(0, 0); 2 * n];
    let mut online_ps = vec![];
    let mut online_cnt = vec![0; n];
    for i in 0..n {
        for j in 0..2 {
            let x = read::<i32>();
            let y = read::<i32>();
            ps[i * 2 + j] = (x, y);
            if x == 0 || y == 0 || x == w || y == h {
                let mut d = 0;
                if y == 0 {
                    d = x;
                } else if x == w {
                    d = w + y;
                } else if y == h {
                    d = w + h + (w - x);
                } else if x == 0 {
                    d = w + h + w + (h - y);
                }
                online_ps.push((d, i, x, y));
                online_cnt[i] += 1;
            }
        }
    }
    online_ps.sort();
    let mut stack = vec![];
    for &(_d, index, _x, _y) in online_ps.iter() {
        if online_cnt[index] == 1 {
            continue;
        }
        if let Some(&last_index) = stack.last() {
            if last_index == index {
                stack.pop();
                continue;
            }
        }
        stack.push(index);
    }
    println!("{}", if stack.len() == 0 { "YES" } else { "NO" });
}