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 (7.3.0) (judge verdict: Wrong Answer)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

r,c,n = map(int,readline().split())
data = list(map(int,read().split()))
p = []
for i in range(n):
    x1,y1,x2,y2 = data[i*4:i*4+4]
    if((x1==0)|(x1==r)|(y1==0)|(x1==c))&((x2==0)|(x2==r)|(y2==0)|(y2==c)):
        for x,y in zip([x1,x2],[y1,y2]):
            num = 0
            if(x==0):
                num = y
            elif(x==r):
                num = r+2*c-y
            elif(y==0):
                num = 2*(r+c)-x
            else:
                num = c+x
            p.append([num,i])

p.sort()
d = []
for _,i in p:
    if(not d):
        d.append(i)
    else:
        right = d.pop()
        if(right != i):
            d.append(right)
            d.append(i)

if(len(d)==0):
    print('YES')
else:
    print('NO')