Connected?

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.

Examples

Input

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

Output

YES

Input

2 2 4 0 0 2 2 2 0 0 1 0 2 1 2 1 1 2 1

Output

NO

Input

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

Output

YES

Input

1 1 2 0 0 1 1 1 0 0 1

Output

NO

inputFormat

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}

outputFormat

Output

Print YES if the objective is achievable; print NO otherwise.

Examples

Input

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

Output

YES

Input

2 2 4 0 0 2 2 2 0 0 1 0 2 1 2 1 1 2 1

Output

NO

Input

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

Output

YES

Input

1 1 2 0 0 1 1 1 0 0 1

Output

NO

样例

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

YES