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 = 'w, h, n = list(map(int, input().split()))\n\npos = []\nfor i in range(n):\n    x1, y1, x2, y2 = list(map(int, input().split()))\n    if (x1 in [0, w] or y1 in [0, h]) and (x2 in [0, w] or y2 in [0, h]):\n        pos.append((x1, y1, i))\n        pos.append((x2, y2, i))\n\npos.sort(key=lambda v: v[0]) # top →\nedge = [v[-1] for v in pos if v[1] == 0 and v[0] != 0]\n\npos.sort(key=lambda v: v[1]) # left ↓\nedge += [v[-1] for v in pos if v[0] == w and v[1] != 0]\n\npos.sort(key=lambda v: v[0], reverse=True) # bottom ←\nedge += [v[-1] for v in pos if v[1] == h and v[0] != w]\n\npos.sort(key=lambda v: v[1], reverse=True) # right ↑\nedge += [v[-1] for v in pos if v[0] == 0 and v[1] != h]\n\n# for i in range(len(edge) - 1):\n#     if edge[i] == edge[i + 1]:\n#         break\n# for j in range(len(edge) // 2):\n#     if edge[(i + j + 1) % n] != edge[(i - j + n) % n]:\n#         print("NO")\n#         break\n# else:\n#     print("YES")\n\n# print(edge)\nhist = [None] * n\nstep = 0\nfor v in edge:\n    if hist[v] is None:\n        hist[v] = step + 1\n        step += 1\n    else:\n        if hist[v] != step:\n            print("NO")\n            break\n        step -= 1\nelse:\n    print("YES")\n\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13577