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)

fn get_line() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().to_string()
}

fn reads<T>() -> Vec<T>
    where
        T: std::str::FromStr,
        <T as std::str::FromStr>::Err: std::fmt::Debug {
    get_line().split(' ').map(|x| x.parse().unwrap()).collect()
}

use std::cmp;

fn main() {
    let rcn = reads();

    let mut xs: Vec<(usize, usize, bool)> = vec![];

    let convf = |&x, &y| {
        if x == 0 {
            Some(2 * (rcn[0] + rcn[1]) - y)
        }
        else if x == rcn[0] {
            Some(x + y)
        }
        else if y == 0 {
            Some(x)
        }
        else if y == rcn[1] {
            Some(rcn[0] * 2 + y - x)
        }
        else {
            None
        }
    };

    for i in 0..rcn[2] {
        let xys = reads();

        let vm1 = convf(&xys[0], &xys[1]);
        let vm2 = convf(&xys[2], &xys[3]);

        if let (Some(v1), Some(v2)) = (vm1, vm2) {
            xs.push((cmp::min(v1, v2), i, true));
            xs.push((cmp::max(v1, v2), i, false));
        }
    }

    xs.sort();

    let mut s = vec![];

    let mut res = true;

    for (_, i, b) in xs {
        if b {
            s.push(i);
        }
        else {
            let j = s.pop().unwrap();

            if j != i {
                res = false;
                break;
            }
        }
    }

    println!("{}",
        if res {
            "YES"
        }
        else {
            "NO"
        }
    );
}