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 = '#!usr/bin/env python3\nfrom collections import defaultdict,deque\nfrom heapq import heappush, heappop\nimport sys\nimport math\nimport bisect\nimport random\ndef LI(): return [int(x) for x in sys.stdin.readline().split()]\ndef I(): return int(sys.stdin.readline())\ndef LS():return [list(x) for x in sys.stdin.readline().split()]\ndef S():\n    res = list(sys.stdin.readline())\n    if res[-1] == "\\n":\n        return res[:-1]\n    return res\ndef IR(n):\n    return [I() for i in range(n)]\ndef LIR(n):\n    return [LI() for i in range(n)]\ndef SR(n):\n    return [S() for i in range(n)]\ndef LSR(n):\n    return [LS() for i in range(n)]\n\nsys.setrecursionlimit(1000000)\nmod = 1000000007\n\ndef solve():\n    def check(x,y):\n        return (x == 0)|(x == w)|(y == 0)|(y == h)\n\n    w,h,n = LI()\n    px0 = []\n    pxw = []\n    py0 = []\n    pyh = []\n    for i in range(1,n+1):\n        x,y,s,t = LI()\n        if check(x,y)&check(s,t):\n            if x == 0:\n                px0.append((y,i))\n            elif x == w:\n                pxw.append((-y,i))\n            elif y == 0:\n                py0.append((-x,i))\n            else:\n                pyh.append((x,i))\n            if s == 0:\n                px0.append((t,i))\n            elif s == w:\n                pxw.append((-t,i))\n            elif t == 0:\n                py0.append((-s,i))\n            else:\n                pyh.append((s,i))\n    px0.sort()\n    pxw.sort()\n    py0.sort()\n    pyh.sort()\n    p = px0+pyh+pxw+py0\n    q = deque()\n    for x, i in p:\n        if q:\n            qi = q.pop()\n            if qi != i:\n                q.append(qi)\n                q.append(i)\n        else:\n            q.append(i)\n    if q:\n        print("NO")\n    else:\n        print("YES")\n    return\n\n#Solve\ndef __starting_point():\n    solve()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17311