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
from collections import deque

def f(x, y):
    if x == 0:
        return y
    if y == 0:
        return -x
    if x == r:
        return -(x + y)
    if y == c:
        return x + y

r, c, n = map(int, input().split())
xy = []
lxy = 0
for i in range(n):
    x1, y1, x2, y2 = map(int, input().split())
    d = []
    if min(x1, y1) == 0 or x1 == r or y1 == c:
        d.append([f(x1, y1), i])
    if min(x2, y2) == 0 or x2 == r or y2 == c:
        d.append([f(x2, y2), i])
    if len(d) == 2:
        xy.append(d[0])
        xy.append(d[1])
        lxy += 2
xy.sort()
q = deque()
lq = -1
for i in range(lxy):
    if not q:
        q.append(xy[i][1])
        lq += 1
    else:
        if q[lq] == xy[i][1]:
            q.pop()
            lq -= 1
        else:
            q.append(xy[i][1])
            lq += 1
print("YES" if not q else "NO")