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 sys import setrecursionlimit, stderr\nfrom functools import reduce\nfrom itertools import *\nfrom collections import *\nfrom bisect import *\n\ndef read():\n  return int(input())\n \ndef reads():\n  return [int(x) for x in input().split()]\n\nR, C, N = reads()\n\ndef edge(x, y):\n  return x == 0 or x == R or y == 0 or y == C\n\ndef flat(x, y):\n  assert edge(x, y)\n  if y == 0:\n    return x\n  elif x == R:\n    return R + y\n  elif y == C:\n    return R + C + (R - x)\n  else:\n    assert x == 0\n    return 2 * R + C + (C - y)\n\nps = []\nfor i in range(N):\n  x1, y1, x2, y2 = reads()\n  if edge(x1, y1) and edge(x2, y2):\n    ps.append((flat(x1, y1), i))\n    ps.append((flat(x2, y2), i))\nps.sort()\n\nstack = []\nfor _, i in ps:\n  if len(stack) > 0 and stack[-1] == i:\n    stack.pop()\n  else:\n    stack.append(i)\n\nprint("YES" if len(stack) == 0 else "NO")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14623