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 = 'R, C, N = list(map(int, input().split()))\nUP, RIGHT, DOWN, LEFT = [], [], [], []\nfor i in range(N):\n    x1, y1, x2, y2 = list(map(int, input().split()))\n\n    # 2つとも周上にない\n    if 0 < x1 < R and 0 < y1 < C:\n        continue\n    if 0 < x2 < R and 0 < y2 < C:\n        continue\n\n    # 2つとも周回上にある\n    if x1 == 0: UP.append([i, y1])\n    elif x1 == R: DOWN.append([i, y1])\n    elif y1 == 0: LEFT.append([i, x1])\n    elif y1 == C: RIGHT.append([i, x1])\n\n    if x2 == 0: UP.append([i, y2])\n    elif x2 == R: DOWN.append([i, y2])\n    elif y2 == 0: LEFT.append([i, x2])\n    elif y2 == C: RIGHT.append([i, x2])\n\n\n# 時計回りに探索できるようにする\nUP.sort(key=lambda x: x[1])\nRIGHT.sort(key=lambda x: x[1])\nDOWN.sort(key=lambda x: x[1], reverse=True)\nLEFT.sort(key=lambda x: x[1], reverse=True)\n\n# 全体を連結\nNumbers = UP + RIGHT + DOWN + LEFT\n\n# 時計回りに探索\nstack = []\nfor n, z in Numbers:\n    if stack and stack[-1] == n:\n        stack.pop()\n\n    else:\n        stack.append(n)\nprint(("NO" if stack else "YES"))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 13985