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

def main():
  r, c, n = map(int, input().split())
  L = []
  def trans(x, y):
    z = None
    if x == 0:
      z = y
    if y == c:
      z = c + x
    if x == r:
      z = c + r + c - y
    if y == 0:
      z = 2*r + 2*c - x
    return z

  for _ in range(n):
    x1, y1, x2, y2 = map(int, input().split())
    z1 = trans(x1, y1)
    z2 = trans(x2, y2)
    if z1 is not None and z2 is not None:
      L.append((z1, z2))
      L.append((z2, z1))
  L.sort()
  cnt = 0
  D = dict()
  for z1, z2 in L:
    if z1 < z2:
      cnt += 1
      D[z1] = cnt
    else:
      if D[z2] != cnt:
        print("NO")
        exit()
      cnt -= 1
  print("YES")
if __name__ == "__main__":
  main()