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())
points = []
xx = [0, r]
yy = [0, c]
def add(x, y):
    if x == 0:
        points.append(r*2+c+c-y)
    elif x == r:
        points.append(r+y)
    elif y == 0:
        points.append(x)
    else:
        points.append(r+c+r-x)
for i in range(n):
    x0, y0, x1, y1 = map(int, input().split())
    if (x0 in xx or y0 in yy) and (x1 in xx or y1 in yy):
        add(x0, y0)
        add(x1, y1)
index = list(range(len(points)))
index.sort(key = lambda a:points[a])
que = []
flag = True
for i in index:
    if que and que[-1]//2 == i//2:
        que.pop()
    else:
        que.append(i)
if que:
    print('NO')
else:
    print('YES')
    