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
R, C, N = map(int, input().split())
UP, RIGHT, DOWN, LEFT = [], [], [], []
for i in range(N):
    x1, y1, x2, y2 = map(int, input().split())

    # 2つとも周上にない
    if 0 < x1 < R and 0 < y1 < C:
        continue
    if 0 < x2 < R and 0 < y2 < C:
        continue

    # 2つとも周回上にある
    if x1 == 0: UP.append([i, y1])
    elif x1 == R: DOWN.append([i, y1])
    elif y1 == 0: LEFT.append([i, x1])
    elif y1 == C: RIGHT.append([i, x1])

    if x2 == 0: UP.append([i, y2])
    elif x2 == R: DOWN.append([i, y2])
    elif y2 == 0: LEFT.append([i, x2])
    elif y2 == C: RIGHT.append([i, x2])


# 時計回りに探索できるようにする
UP.sort(key=lambda x: x[1])
RIGHT.sort(key=lambda x: x[1])
DOWN.sort(key=lambda x: x[1], reverse=True)
LEFT.sort(key=lambda x: x[1], reverse=True)

# 全体を連結
Numbers = UP + RIGHT + DOWN + LEFT

# 時計回りに探索
stack = []
for n, z in Numbers:
    if stack and stack[-1] == n:
        stack.pop()

    else:
        stack.append(n)
print("NO" if stack else "YES")
