200762: [AtCoder]ARC076 E - Connected?

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