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\n\nsys.setrecursionlimit(10 ** 6)\nint1 = lambda x: int(x) - 1\np2D = lambda x: print(*x, sep="\\n")\ndef MI(): return map(int, sys.stdin.readline().split())\ndef LI(): return list(map(int, sys.stdin.readline().split()))\ndef LLI(rows_number): return [LI() for _ in range(rows_number)]\n\ndef main():\n    h, w, n = MI()\n    points = []\n    cnt = 0\n    # 2点とも周上にある組のみ残す\n    # 原点（左上）から反時計回りに移動した距離と点の通し番号を記録\n    for _ in range(n):\n        i0, j0, i1, j1 = MI()\n        if (0 < i0 < h and 0 < j0 < w) or (0 < i1 < h and 0 < j1 < w): continue\n        for i, j in [(i0, j0), (i1, j1)]:\n            if j == 0 or i == h:\n                d = i + j\n            else:\n                d = 2 * (h + w) - i - j\n            points.append([d, cnt])\n        cnt += 1\n    points.sort()\n    first = [True] * cnt\n    visited = []\n    # ABABのように２つの区間がずれて重なっていたらNO\n    # ABBAのように完全に含まれるのはセーフ\n    for d, pi in points:\n        if first[pi]:\n            visited.append(pi)\n            first[pi] = False\n        else:\n            last_pi = visited.pop()\n            if pi != last_pi:\n                print("NO")\n                return\n    print("YES")\n\nmain()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 15071