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())
a = [list(map(int, input().split())) for _ in range(n)]
iru = []
for i in range(n):
  if ((a[i][0] == 0 or a[i][0] == r or a[i][1] == 0 or a[i][1] == c) and (a[i][2] == 0 or a[i][2] == r or a[i][3] == 0 or a[i][3] == c)):
    b = a[i]
    b1 = [b[0],b[1]]
    b2 = [b[2],b[3]]
    if b1[0] == 0:
      b1 = b1[1]
    elif b1[1] == c:
      b1 = b1[0] + b1[1]
    elif b1[0] == r:
      b1 = c +r+c -b1[1]
    else:
      b1 = c*2 + r*2 - b1[0]
      
    if b2[0] == 0:
      b2 = b2[1]
    elif b2[1] == c:
      b2 = b2[0] + b2[1]
    elif b2[0] == r:
      b2 = c*2 +r -b2[1]
    else:
      b2 = c*2 + r*2 - b2[0]
    if b1 > b2:
      tmp = b1 +0
      b1 = b2 +0
      b2 = tmp + 0
    iru.append([b1,b2])
iru = sorted(iru)
ato = 0
stack = [r+r+c+c]
flag = 'YES'
for a,b in iru:
  while a >= stack[-1]:
    stack.pop()
 
  if b > stack[-1]:
    flag = 'NO'
    break
  else:
    stack.append(b)
 
print(flag)