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)

from sys import exit, setrecursionlimit, stderr
from functools import reduce
from itertools import *
from collections import *
from bisect import *

def read():
  return int(input())
 
def reads():
  return [int(x) for x in input().split()]

R, C, N = reads()

def edge(x, y):
  return x == 0 or x == R or y == 0 or y == C

def flat(x, y):
  assert edge(x, y)
  if y == 0:
    return x
  elif x == R:
    return R + y
  elif y == C:
    return R + C + (R - x)
  else:
    assert x == 0
    return 2 * R + C + (C - y)

ps = []
for i in range(N):
  x1, y1, x2, y2 = reads()
  if edge(x1, y1) and edge(x2, y2):
    ps.append((flat(x1, y1), i))
    ps.append((flat(x2, y2), i))
ps.sort()

stack = []
for _, i in ps:
  if len(stack) > 0 and stack[-1] == i:
    stack.pop()
  else:
    stack.append(i)

print("YES" if len(stack) == 0 else "NO")