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 PyPy3 (2.4.0) (judge verdict: Accepted)

R,C,N=map(int,input().split())
points=[list(map(int,input().split())) for i in range(N)]
def circ(x,y):
    if y==0:
        return x
    elif x==R:
        return y+R
    elif y==C:
        return R+C+R-x
    elif x==0:
        return R+C+R+C-y
    else:
        return -1

L=[]
for i in range(N):
    x1,y1,x2,y2=points[i]
    if circ(x1,y1)==-1 or circ(x2,y2)==-1:
        continue
    L.append((circ(x1,y1),i))
    L.append((circ(x2,y2),i))
#board=[[circ(x,y) for y in range(C+1)] for x in range(R+1)]
R=[s[1] for s in sorted(L)]
X=[]
for i in R:
    if len(X)==0:
        X.append(i)
    else:
        if X[-1]==i:
            X.pop()
        else:
            X.append(i)
if len(X)==0:
    print("YES")
else:
    print("NO")