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

-----Sample Output-----
YES


The above figure shows a possible solution.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

ns = {"__name__": "__main__"}
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "from operator import itemgetter\nimport collections\nr,c,n=map(int,input().split())\nl=[list(map(int,input().split())) for i in range(n)]\ne1=[];e2=[];e3=[];e4=[]\nfor i in range(n):\n  if (l[i][0]==0 or l[i][0]==r or l[i][1]==0 or l[i][1]==c) and (l[i][2]==0 or l[i][2]==r or l[i][3]==0 or l[i][3]==c):\n    if l[i][0]==0 and l[i][1]!=c:\n      e1.append([i+1,l[i][0],l[i][1]])\n    elif l[i][1]==c and l[i][0]!=r:\n      e2.append([i+1,l[i][0],l[i][1]])\n    elif l[i][0]==r and l[i][1]!=0:\n      e3.append([i+1,l[i][0],l[i][1]])\n    else:\n      e4.append([i+1,l[i][0],l[i][1]])\n    if l[i][2]==0 and l[i][3]!=c:\n      e1.append([i+1,l[i][2],l[i][3]])\n    elif l[i][3]==c and l[i][2]!=r:\n      e2.append([i+1,l[i][2],l[i][3]])\n    elif l[i][2]==r and l[i][3]!=0:\n      e3.append([i+1,l[i][2],l[i][3]])\n    else:\n      e4.append([i+1,l[i][2],l[i][3]])\ne1=sorted(e1,key=itemgetter(2))\ne2=sorted(e2,key=itemgetter(1))\ne3=sorted(e3,key=itemgetter(2))\ne4=sorted(e4,key=itemgetter(1))\ne3.reverse()\ne4.reverse()\ne=e1+e2+e3+e4\n\nq=[]\nq=collections.deque(q)\nfor i in range(len(e)):\n  if len(q)==0:\n    q.append(e[i][0])\n  else:\n    if q[-1]==e[i][0]:\n      q.pop()\n    else:\n      q.append(e[i][0])\nif len(q)==0:\n  print('YES')\nelse:\n  print('NO')"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15175