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
def put(i, x, y):
    if x == 0:
        on_top.append((y, i))
    elif x == r:
        on_bottom.append((y, i))
    elif y == 0:
        on_left.append((x, i))
    else:
        on_right.append((x, i))


on_top, on_bottom, on_left, on_right = [], [], [], []

r, c, n = map(int, input().split())
for i in range(n):
    x1, y1, x2, y2 = map(int, input().split())
    if 0 < x1 < r and 0 < y1 < c:
        continue
    if 0 < x2 < r and 0 < y2 < c:
        continue
    put(i, x1, y1)
    put(i, x2, y2)
on_top.sort()
on_bottom.sort(reverse=True)
on_left.sort(reverse=True)
on_right.sort()
stack = []
for on_edge in [on_top, on_right, on_bottom, on_left]:
    for p, i in on_edge:
        if stack and stack[-1] == i:
            stack.pop()
        else:
            stack.append(i)

print('NO' if stack else 'YES')
