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\ninput = lambda: sys.stdin.readline().rstrip()\nR, C, N = map(int, input().split())\nX = {0, R}\nY = {0, C}\n\nZ = []\nfor i in range(N):\n    x1, y1, x2, y2 = map(int, input().split())\n    if (x1 == 0 or x1 == R or y1 == 0 or y1 == C) and (x2 == 0 or x2 == R or y2 == 0 or y2 == C):\n        Z.append((x1, y1, x2, y2))\n        X.add(x1)\n        X.add(x2)\n        Y.add(y1)\n        Y.add(y2)\n\nDX = {a: i for i, a in enumerate(sorted(list(X)))}\nDY = {a: i for i, a in enumerate(sorted(list(Y)))}\nR, C = DX[R], DY[C]\n\ndef calc(a, b):\n    if b == 0:\n        return a\n    if a == R:\n        return b + R\n    if b == C:\n        return R + C + (R - a)\n    if a == 0:\n        return R + C + R + (C - b)\n\nA = []\nfor i, (x1, y1, x2, y2) in enumerate(Z):\n    x3, y3, x4, y4 = DX[x1], DY[y1], DX[x2], DY[y2]\n    A.append((calc(x3, y3), i))\n    A.append((calc(x4, y4), i))\n\nA = [l[1] for l in sorted(A, key = lambda x: x[0])]\nB = []\n\nwhile A:\n    while len(B) and A[-1] == B[-1]:\n        A.pop()\n        B.pop()\n    if A:\n        B.append(A.pop())\n\nprint("NO" if len(B) else "YES")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14591