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 = "#!/usr/bin/env python3\n\n\ndef add(bound, r, c, x, y, i):\n    if x == 0:\n        bound.append((0, y, i))\n    elif y == c:\n        bound.append((1, x, i))\n    elif x == r:\n        bound.append((2, c - y, i))\n    else:\n        bound.append((3, r - x, i))\n\n\ndef solve(bound):\n\n    if not bound:\n        return True\n\n    bound.sort()\n    st = [0] * len(bound)\n    p = -1\n\n    for _, _, i in bound:\n        if 0 <= p and st[p] == i:\n            p -= 1\n        else:\n            p += 1\n            st[p] = i\n\n    return p == -1\n\n\ndef main():\n    r, c, n = input().split()\n    r = int(r)\n    c = int(c)\n    n = int(n)\n    bound = []\n    for i in range(n):\n        x1, y1, x2, y2 = input().split()\n        x1 = int(x1)\n        y1 = int(y1)\n        x2 = int(x2)\n        y2 = int(y2)\n        if (x1 % r == 0 or y1 % c == 0) and (x2 % r == 0 or y2 % c == 0):\n            add(bound, r, c, x1, y1, i)\n            add(bound, r, c, x2, y2, i)\n\n\n    print(('YES' if solve(bound) else 'NO'))\n\n\ndef __starting_point():\n    main()\n\n\n__starting_point()"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14427