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 random\nimport sys\ninput = sys.stdin.readline\n\n\nclass BIT():\n    """区間加算、一点取得クエリをそれぞれO(logN)で答える\n    add: 区間[l, r)にvalを加える\n    get_val: i番目の値を求める\n    i, l, rは0-indexed\n    """\n    def __init__(self, n):\n        self.n = n\n        self.bit = [0] * (n + 1)\n\n    def _add(self, i, val):\n        while i > 0:\n            self.bit[i] += val\n            i -= i & -i\n\n    def get_val(self, i):\n        """i番目の値を求める"""\n        i = i + 1\n        s = 0\n        while i <= self.n:\n            s += self.bit[i]\n            i += i & -i\n        return s\n\n    def add(self, l, r, val):\n        """区間[l, r)にvalを加える"""\n        self._add(r, val)\n        self._add(l, -val)\n\n\nr, c, n = map(int, input().split())\ninfo = [list(map(int, input().split())) for i in range(n)]\n\ndef solve(x1, y1):\n    if y1 == 0:\n        return x1\n    if x1 == r:\n        return r + y1\n    if y1 == c:\n        return r + c + (r-x1)\n    if x1 == 0:\n        return r + c + r + (c-y1)\n\ndef compress(array):\n    set_ = set([])\n    for i in range(len(array)):\n        a, b = array[i]\n        set_.add(a)\n        set_.add(b)\n    memo = {value : index for index, value in enumerate(sorted(list(set_)))}\n    max_ = 0\n    for i in range(len(array)):\n        array[i][0] = memo[array[i][0]]\n        array[i][1] = memo[array[i][1]]\n        max_ = max(max_, *array[i])\n    return max_, array\n\nquery = []\nfor i in range(n):\n    x1, y1, x2, y2 = info[i]\n    if (x1 % r == 0 or y1 % c == 0) and (x2 % r == 0 or y2 % c == 0):\n        pos1, pos2 = solve(x1, y1), solve(x2, y2)\n        if pos1 > pos2:\n            pos1, pos2 = pos2, pos1\n        query.append([pos1, pos2 + 1])\n\nm, query = compress(query)\nbit = BIT(m)  \nfor i in range(len(query)):\n    begin, end = query[i]\n    if bit.get_val(begin) != bit.get_val(end - 1):\n        print("NO")\n        return\n    tmp = random.randrange(0, 10**18)\n    bit.add(begin, end, tmp)\nprint("YES")'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: