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, raw_input().split())
x1 = []
y1 = []
x2 = []
y2 = []
for i in xrange(n): 
  xx1, yy1, xx2, yy2 = map(int, raw_input().split())
  x1.append(xx1)
  y1.append(yy1)
  x2.append(xx2)
  y2.append(yy2)

t = []
b = []
l = []
r = []

def add(x, y, i):
  if x == 0:
    t.append((i, y))
  elif x == R:
    b.append((i, y))
  elif y == 0:
    l.append((i, x))
  elif y == C:
    r.append((i, x))


for i in xrange(n):
  add(x1[i], y1[i], i)
  add(x2[i], y2[i], i)

t = sorted(t, key=lambda x : x[1])    
r = sorted(r, key=lambda x : x[1])
b = sorted(b, key=lambda x : x[1], reverse=True)
l = sorted(l, key=lambda x : x[1], reverse=True)

lis = []
lis.extend(t)
lis.extend(r)
lis.extend(b)
lis.extend(l)

lis = map(lambda x : x[0], lis)

cnt = {}
for i in lis:
  if not i in cnt:
    cnt[i] = 0
  cnt[i] += 1

lis = filter(lambda x : cnt[x] == 2, lis)

stk = []
for i in lis:
  if len(stk) == 0 or stk[-1] != i:
    stk.append(i)
  else:
    stk.pop()

if len(stk) == 0:
  print("YES")
else:
  print("NO")
