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, math, collections, heapq, itertools\nF = sys.stdin\ndef single_input(): return F.readline().strip("\\n")\ndef line_input(): return F.readline().strip("\\n").split()\n\ndef solve():\n    R, C, N = map(int, line_input())\n    u, l, r, d = [], [], [], []\n    for i in range(N):\n        x, y, z, w = map(int, line_input())\n        if x == 0:\n            if z == 0: \n                u.append((y, i))\n                u.append((w, i))\n            elif w == C:\n                u.append((y, i))\n                r.append((z, i))\n            elif z == R:\n                u.append((y, i))\n                d.append((w, i))\n            elif w == 0:\n                u.append((y, i))\n                l.append((z, i))\n        elif x == R:\n            if z == 0: \n                d.append((y, i))\n                u.append((w, i))\n            elif w == C:\n                d.append((y, i))\n                r.append((z, i))\n            elif z == R:\n                d.append((y, i))\n                d.append((w, i))\n            elif w == 0:\n                d.append((y, i))\n                l.append((z, i))\n        elif y == 0:\n            if z == 0: \n                l.append((x, i))\n                u.append((w, i))\n            elif w == C:\n                l.append((x, i))\n                r.append((z, i))\n            elif z == R:\n                l.append((x, i))\n                d.append((w, i))\n            elif w == 0:\n                l.append((x, i))\n                l.append((z, i))\n        elif y == C:\n            if z == 0: \n                r.append((x, i))\n                u.append((w, i))\n            elif w == C:\n                r.append((x, i))\n                r.append((z, i))\n            elif z == R:\n                r.append((x, i))\n                d.append((w, i))\n            elif w == 0:\n                r.append((x, i))\n                l.append((z, i))\n    u.sort()\n    r.sort()\n    d.sort(reverse = True)\n    l.sort(reverse = True)\n\n    s = []\n    used = set()\n    crossed = True\n    for point, n in u:\n        if n not in used:\n            s.append(n)\n            used |= {n}\n        else:\n            if s[-1] != n: break\n            else: s.pop()\n    else:\n        for point, n in r:\n            if n not in used:\n                s.append(n)\n                used |= {n}\n            else:\n                if s[-1] != n: break\n                else: s.pop()\n        else:\n            for point, n in d:\n                if n not in used:\n                    s.append(n)\n                    used |= {n}\n                else:\n                    if s[-1] != n: break\n                    else: s.pop()\n            else:\n                for point, n in l:\n                    if n not in used:\n                        s.append(n)\n                        used |= {n}\n                    else:\n                        if s[-1] != n: break\n                        else: s.pop()\n                else: crossed = False\n\n    print("NO" if crossed else "YES")\n                            \n    return 0\n  \ndef __starting_point():\n    solve()\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 17083