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.

Examples

Input

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2


Output

YES


Input

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1


Output

NO


Input

5 5 7
0 0 2 4
2 3 4 5
3 5 5 2
5 5 5 4
0 3 5 1
2 2 4 4
0 5 4 1


Output

YES


Input

1 1 2
0 0 1 1
1 0 0 1


Output

NO
import os
import sys
from collections import deque, Counter

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(10 ** 9)
INF = float("inf")
IINF = 10 ** 18
MOD = 10 ** 9 + 7
# MOD = 998244353


R, C, N = list(map(int, sys.stdin.buffer.readline().split()))
XY = [list(map(int, sys.stdin.buffer.readline().split())) for _ in range(N)]

# 入力と答えの制約より、もし長方形の制限がなければ任意の点まで行ける
# 長方形の辺上にある点だけ考えればいい

p1 = []
p2 = []
p3 = []
p4 = []
for i, (x1, y1, x2, y2) in enumerate(XY):
    for x, y in ((x1, y1), (x2, y2)):
        if y == 0:
            p1.append((x, i))
        elif x == R:
            p2.append((y, i))
        elif y == C:
            p3.append((x, i))
        elif x == 0:
            p4.append((y, i))
# 順番に並ぶようにする
p1.sort()
p2.sort()
p3.sort(reverse=True)
p4.sort(reverse=True)

points = p1 + p2 + p3 + p4
counts = Counter([i for _, i in points])
que = deque()
for _, i in points:
    if counts[i] <= 1:
        continue
    if que and que[-1] == i:
        que.pop()
    else:
        que.append(i)

while len(que) >= 2 and que[0] == que[-1]:
    que.popleft()
    que.pop()

ok = len(que) == 0
if ok:
    print('YES')
else:
    print('NO')
