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 = 'R, C, n = list(map(int, input().split()))\nx1 = []\ny1 = []\nx2 = []\ny2 = []\nfor i in range(n): \n  xx1, yy1, xx2, yy2 = list(map(int, input().split()))\n  x1.append(xx1)\n  y1.append(yy1)\n  x2.append(xx2)\n  y2.append(yy2)\n\nt = []\nb = []\nl = []\nr = []\n\ndef add(x, y, i):\n  if x == 0:\n    t.append((i, y))\n  elif x == R:\n    b.append((i, y))\n  elif y == 0:\n    l.append((i, x))\n  elif y == C:\n    r.append((i, x))\n\n\nfor i in range(n):\n  add(x1[i], y1[i], i)\n  add(x2[i], y2[i], i)\n\nt = sorted(t, key=lambda x : x[1])    \nr = sorted(r, key=lambda x : x[1])\nb = sorted(b, key=lambda x : x[1], reverse=True)\nl = sorted(l, key=lambda x : x[1], reverse=True)\n\nlis = []\nlis.extend(t)\nlis.extend(r)\nlis.extend(b)\nlis.extend(l)\n\nlis = [x[0] for x in lis]\n\ncnt = {}\nfor i in lis:\n  if not i in cnt:\n    cnt[i] = 0\n  cnt[i] += 1\n\nlis = [x for x in lis if cnt[x] == 2]\n\nstk = []\nfor i in lis:\n  if len(stk) == 0 or stk[-1] != i:\n    stk.append(i)\n  else:\n    stk.pop()\n\nif len(stk) == 0:\n  print("YES")\nelse:\n  print("NO")\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13937