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 = '# coding: utf-8\nimport array, bisect, collections, copy, heapq, itertools, math, random, re, string, sys, time\nsys.setrecursionlimit(10 ** 7)\nINF = 10 ** 20\nMOD = 10 ** 9 + 7\n\n\ndef II(): return int(input())\ndef ILI(): return list(map(int, input().split()))\ndef IAI(LINE): return [ILI() for __ in range(LINE)]\ndef IDI(): return {key: value for key, value in ILI()}\n\n\ndef read():\n    R, C, N = ILI()\n    num_point = []\n    for __ in range(N):\n        x_1, y_1, x_2, y_2 = ILI()\n        num_point.append([(x_1, y_1), (x_2, y_2)])\n    return R, C, N, num_point\n\n\n# 周上を (0, 0) を原点として反時計回りに 1 本の数直線とした時の point の座標を返す．\n# 周上にあるかの判定も行う．\ndef change_edge_point(R, C, point):\n    x, y = point\n    if x == 0:\n        return R * 2 + C + (C - y)\n    if x == R:\n        return R + y\n    if y == 0:\n        return x\n    if y == C:\n        return R + C + (R - x)\n\n\ndef solve(R, C, N, num_point):\n    point_double = []\n    for ind, point in enumerate(num_point):\n        p_1, p_2 = point\n        if ((p_1[0] == 0 or p_1[0] == R) or (p_1[1] == 0 or p_1[1] == C)) and ((p_2[0] == 0 or p_2[0] == R) or (p_2[1] == 0 or p_2[1] == C)):\n            point_double.append((ind + 1, change_edge_point(R, C, p_1)))\n            point_double.append((ind + 1, change_edge_point(R, C, p_2)))\n    point_double.sort(key=lambda  x: x[1])\n    stack = []\n    for point in point_double:\n        if len(stack) == 0:\n            stack.append(point[0])\n            continue\n        if point[0] == stack[-1]:\n            stack.pop()\n        else:\n            stack.append(point[0])\n    \n    if len(stack) == 0:\n        return "YES"\n    else:\n        return "NO"\n    \n\ndef main():\n    params = read()\n    print((solve(*params)))\n\n\ndef __starting_point():\n    main()\n\n__starting_point()'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 178031