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 main():\n    from bisect import bisect_left as bl\n\n    class BIT():\n        def __init__(self, member):\n            self.member_list = sorted(member)\n            self.member_dict = {v: i+1 for i, v in enumerate(self.member_list)}\n            self.n = len(member)\n            self.maxmember = self.member_list[-1]\n            self.minmember = self.member_list[0]\n            self.maxbit = 2**(len(bin(self.n))-3)\n            self.bit = [0]*(self.n+1)\n            self.allsum = 0\n\n        # 要素iにvを追加する\n        def add(self, i, v):\n            x = self.member_dict[i]\n            self.allsum += v\n            while x < self.n + 1:\n                self.bit[x] += v\n                x += x & (-x)\n\n        # 位置0からiまでの和(sum(bit[:i]))を計算する\n        def sum(self, i):\n            ret = 0\n            x = i\n            while x > 0:\n                ret += self.bit[x]\n                x -= x & (-x)\n            return ret\n\n        # 位置iからjまでの和(sum(bit[i:j]))を計算する\n        def sum_range(self, i, j):\n            return self.sum(j) - self.sum(i)\n\n        # 和がw以上となる最小のインデックスを求める\n        def lowerbound(self, w):\n            if w <= 0:\n                return 0\n            x, k = 0, self.maxbit\n            while k:\n                if x+k <= self.n and self.bit[x+k] < w:\n                    w -= self.bit[x+k]\n                    x += k\n                k //= 2\n            return x\n\n        # vに一番近いv以上の値を求める\n        def greater(self, v):\n            if v > self.maxmember:\n                return None\n            p = self.sum(bl(self.member_list, v))\n            if p == self.allsum:\n                return None\n            return self.member_list[self.lowerbound(p+1)]\n\n        # vに一番近いv以下の値を求める\n        def smaller(self, v):\n            if v < self.minmember:\n                return None\n            b = bl(self.member_list, v)\n            if b == self.n:\n                b -= 1\n            elif self.member_list[b] != v:\n                b -= 1\n            p = self.sum(b+1)\n            if p == 0:\n                return None\n            return self.member_list[self.lowerbound(p)]\n\n    r, c, n = list(map(int, input().split()))\n    xyzw = [list(map(int, input().split())) for _ in [0]*n]\n    outer = []\n    for x, y, z, w in xyzw:\n        if x in [0, r] or y in [0, c]:\n            if z in [0, r] or w in [0, c]:\n                if y == 0:\n                    p = x\n                elif x == r:\n                    p = r+y\n                elif y == c:\n                    p = 2*r+c-x\n                else:\n                    p = 2*r+2*c-y\n                if w == 0:\n                    q = z\n                elif z == r:\n                    q = r+w\n                elif w == c:\n                    q = 2*r+c-z\n                else:\n                    q = 2*r+2*c-w\n                if p > q:\n                    p, q = q, p\n                outer.append((p, q))\n\n    member = [i for i, j in outer]+[j for i, j in outer]+[-1]+[2*r+2*c+1]\n    bit = BIT(member)\n    bit.add(-1, 1)\n    bit.add(2*r+2*c+1, 1)\n\n    outer.sort(key=lambda x: x[0]-x[1])\n    for a, b in outer:\n        if bit.greater(a) < b:\n            print("NO")\n            return\n        bit.add(a, 1)\n        bit.add(b, 1)\n    print("YES")\n\n\nmain()\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

```

Measured memory_bytes: 18261