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())
E=[]
for i in range(N):
  x1,y1,x2,y2=map(int,input().split())
  if (0<x1<R and 0<y1<C) or (0<x2<R and 0<y2<C):
    continue
  if y1==0:
    E.append((x1,i))
  elif x1==R:
    E.append((R+y1,i))
  elif y1==C:
    E.append((2*R+C-x1,i))
  elif x1==0:
    E.append((2*R+2*C-y1,i))
  if y2==0:
    E.append((x2,i))
  elif x2==R:
    E.append((R+y2,i))
  elif y2==C:
    E.append((2*R+C-x2,i))
  elif x2==0:
    E.append((2*R+2*C-y2,i))
E.sort()
visited=[False]*N
stack=[]
for p in E:
  if not visited[p[1]]:
    stack.append(p[1])
    visited[p[1]]=True
  elif visited[p[1]]:
    if stack[-1]==p[1]:
      stack.pop()
    else:
      print("NO")
      exit()
print("YES")
  
    