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 = "import sys\nfrom collections import defaultdict\n\n# sys.stdin = open('c1.in')\n\n\ndef read_int_list():\n    return list(map(int, input().split()))\n\n\ndef read_int():\n    return int(input())\n\n\ndef read_str_list():\n    return input().split()\n\n\ndef read_str():\n    return input()\n\n\ndef pos(X, Y):\n    if Y == 0:\n        return X\n    if X == r:\n        return r + Y\n    if Y == c:\n        return r + c + r - X\n    if X == 0:\n        return r + c + r + c - Y\n\n\nr, c, n, = read_int_list()\nx = [0, 0]\ny = [0, 0]\na = []\nfor i in range(n):\n    x[0], y[0], x[1], y[1] = read_int_list()\n    if (x[0] in [0, r] or y[0] in [0, c]) and (x[1] in [0, r] or y[1] in [0, c]):\n        for k in range(2):\n            a.append((pos(x[k], y[k]), i))\nm = len(a) // 2\na.sort()\n\nres = 'YES'\nstarted = set()\ns = []\nfor p, i in a:\n    if i not in started:\n        started.add(i)\n        s.append(i)\n    else:\n        if s[-1] != i:\n            res = 'NO'\n            break\n        s.pop()\n\nprint(res)\n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15057