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

-----Sample Output-----
YES

The above figure shows a possible solution.

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