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())
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:
    if z1 > z2:
      z1, z2 = z2, z1
    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")