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())

def makexy(x1, y1):
    if y1 == 0:
        return x1
    elif x1==R:
        return R+y1
    elif y1 == C:
        return R*2 + C - x1
    else:
        return R*2 + C*2 - y1


XY = []
XY2 = []
D = []
for _ in range(N):
    x1, y1, x2, y2 = map(int, input().split())
    if (x1 in [0, R] or y1 in [0, C]) and (x2 in [0, R] or y2 in [0, C]):
        xy1 = makexy(x1, y1)
        xy2 = makexy(x2, y2)
        xy1, xy2 = sorted((xy1, xy2))
        XY.append((xy1, xy2))
        XY2.append((xy1, 0))
        XY2.append((xy2, 1))
        D.append(xy2-xy1)

#print(XY)
XY.sort()
XY2.sort()
D.sort()

D2 = []
Stack = []
for xy in XY2:
    if xy[1] == 0:
        Stack.append(xy)
    else:
        D2.append(xy[0]-Stack[-1][0])
        del Stack[-1]

D2.sort()
#print(D, D2)
if D == D2:
    print("YES")
else:
    print("NO")
