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 sys
input = lambda: sys.stdin.readline().rstrip()

def calc(a, b):
    if b == 0: return a
    if a == R: return b + R
    if b == C: return R + C + (R - a)
    if a == 0: return R + C + R + (C - b)

R, C, N = map(int, input().split())
A = []
for i in range(N):
    x1, y1, x2, y2 = map(int, input().split())
    if (x1 == 0 or x1 == R or y1 == 0 or y1 == C) and (x2 == 0 or x2 == R or y2 == 0 or y2 == C):
        A.append((calc(x1, y1), i))
        A.append((calc(x2, y2), i))

A = [l[1] for l in sorted(A, key = lambda x: x[0])]
B = []

while A:
    while len(B) and A[-1] == B[-1]:
        A.pop()
        B.pop()
    if A:
        B.append(A.pop())

print("NO" if len(B) else "YES")