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
import sys
input = sys.stdin.readline
r,c,n = map(int,input().split())
xy = [list(map(int,input().split())) for i in range(n)]
ls = []
for x1,y1,x2,y2 in xy:
  if (x1 in (0,r) or y1 in (0,c)) and (x2 in (0,r) or y2 in (0,c)):
    k = []
    for x,y in ((x1,y1),(x2,y2)):
      if x == 0:
        s = 2*r+2*c-y
      if x == r:
        s = r+y
      if y == 0:
        s = x
      if y == c:
        s = 2*r+c-x
      k.append(s)
    t = len(ls)//2+1
    ls.append((k[0],t))
    ls.append((k[1],t))
if not ls:
  print("YES")
  exit()
ls.sort()
lsi = list(map(list,zip(*ls)))[1]
m = len(lsi)
stack = []
for i in lsi:
  if not stack:
    stack.append(i)
  else:
    if stack[-1] == i:
      stack.pop()
    else:
      stack.append(i)
if stack:
  print("NO")
else:
  print("YES")