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 (3.8.2) (judge verdict: Accepted)

r,c,n=map(int,input().split())
def po(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)
q=[]
for i in range(n):
  x1,y1,x2,y2=map(int,input().split())
  if (x1 in [0,r] or y1 in [0,c])and(x2 in [0,r] or y2 in [0,c]):
    q.append((po(x1,y1),i))
    q.append((po(x2,y2),i))
if len(q)==0:exit(print("YES"))
q.sort()
d=[]
for _,i in q:
  if len(d)==0:d.append(i)
  elif d[-1]==i:del d[-1]
  else:d.append(i)
if len(d)==0:print('YES')
else:print('NO')