Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2

Sample Output 1

YES

The above figure shows a possible solution.

Sample Input 2

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1

Sample Output 2

NO

Sample Input 3

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

Sample Output 3

YES

Sample Input 4

1 1 2
0 0 1 1
1 0 0 1

Sample Output 4

NO

Solution in Python (3.4.3) (judge verdict: Accepted)

R,C,N = map(int,input().split())

edges = []

def convert(x,y):
  if y == 0:
    return x
  if x == R:
    return R+y
  if y == C:
    return R+C+R-x
  if x == 0:
    return R+C+R+C-y
  else:
    return -1


for i in range(N):
  a,b,c,d = map(int, input().split())
  
  p,q = convert(a,b),convert(c,d)
  if p >= 0 and q >= 0:
    edges.append((p,q) if p < q else (q,p))

edges.sort()

# print(edges)


stack = [R+R+C+C]
flag = 'YES'
for a,b in edges:
  while a >= stack[-1]:
    stack.pop()

  if b > stack[-1]:
    flag = 'NO'
    break
  else:
    stack.append(b)

print(flag)