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
# coding: utf-8
# Your code here!
import sys
read = sys.stdin.read
readline = sys.stdin.readline

h,w,n, *xyxy = map(int,read().split())

def f(x,y):
    if y==0: return x
    elif x==h: return h+y
    elif y==w: return h+w+h-x
    else: return h+w+h+w-y    

m = iter(xyxy)
res = []
idx = 0
for x1,y1,x2,y2 in zip(m,m,m,m):
    if (x1*(h-x1)==0 or y1*(w-y1)==0) and (x2*(h-x2)==0 or y2*(w-y2)==0):
        res.append((f(x1,y1),idx))
        res.append((f(x2,y2),idx))
        idx += 1


res.sort()
#print(res)

st = []
for d,i in res:
    if st and st[-1] == i:
        st.pop()
    else:
        st.append(i)

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









