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.