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 = 'def calc_pos(x, y, R, C):\n    if y == 0:\n        return x\n    if y == C:\n        return 2 * R + C - x\n    if x == R:\n        return R + y\n    if x == 0:\n        return 2 * R + 2 * C - y\n\ndef read_data():\n    R, C, N = list(map(int, input().split()))\n    pairs = []\n    xys = []\n    idx = 0\n    for i in range(N):\n        x1, y1, x2, y2 = list(map(int, input().split()))\n        xys.append((x1, y1))\n        xys.append((x2, y2))\n        if (x1 != 0 and x1 != R and y1 != 0 and y1 != C) or (x2 != 0 and x2 != R and y2 != 0 and y2 != C):\n            continue\n        a = calc_pos(x1, y1, R, C)\n        b = calc_pos(x2, y2, R, C)\n        pairs.append((a, idx))\n        pairs.append((b, idx))\n        idx += 1\n    pairs.sort()\n    return pairs, xys\n\ndef is_valid(xys):\n    xys.sort()\n    prev_x, prev_y = xys[0]\n    for x, y in xys[1:]:\n        if prev_x == x and prev_y == y:\n            return False\n        prev_x = x\n        prev_y = y\n    return True\n\ndef solve(pairs, xys):\n    if len(xys) == 2:\n        return "YES"\n    if not is_valid(xys):\n        return "NO"    \n    idxs = [i for a, i in pairs]\n    stack = []\n    for idx in idxs:\n        if stack and stack[-1] == idx:\n            stack.pop()\n            continue\n        stack.append(idx)\n    if stack:\n        return "NO"\n    else:\n        return "YES"\n\npairs, xys = read_data()\nprint((solve(pairs, xys)))\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 14463