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 = list(map(int,input().split()))

point = []

def XtoZ(x,y):
    if x==0:
        if y==0:
            return 0
        else:
            return 2*R + 2*C - y
    elif x==R:
        return R + y
    elif y==0:
        return x
    elif y==C:
        return 2*R + C - x

for i in range(N):
    x1,y1,x2,y2 = list(map(int,input().split()))
    if ((x1==0 or x1==R) or (y1==0 or y1==C)) and ((x2==0 or x2==R) or (y2==0 or y2==C)):
        point.append([XtoZ(x1,y1),i])
        point.append([XtoZ(x2,y2),i])

point.sort(key = lambda x:x[0])

flag = [0]*N

from collections import deque

Q = deque()

flag = [True]*N
flag2=False
for p in point:
    if flag[p[1]]:
        Q.append(p[1])
        flag[p[1]] = False
    else:
        if Q.pop()!=p[1]:
            flag2=True
            break

if flag2:
    print("NO")
else:
    print("YES")