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
r, c, n = [int(item) for item in input().split()]
on_edge = [[] for _ in range(4)]
for i in range(n):
    x1, y1, x2, y2 = [int(item) for item in input().split()]
    v1_on_edge = x1 == 0 or x1 == r or y1 == 0 or y1 == c 
    v2_on_edge = x2 == 0 or x2 == r or y2 == 0 or y2 == c 
    if v1_on_edge and v2_on_edge:
        if x1 == 0:
            on_edge[0].append([y1, i])
        elif x1 == r:
            on_edge[2].append([y1, i])
        elif y1 == 0:
            on_edge[3].append([x1, i])
        elif y1 == c:
            on_edge[1].append([x1, i])
        if x2 == 0:
            on_edge[0].append([y2, i])
        elif x2 == r:
            on_edge[2].append([y2, i])
        elif y2 == 0:
            on_edge[3].append([x2, i])
        elif y2 == c:
            on_edge[1].append([x2, i])
for i in range(4):
    if i <= 1:
        on_edge[i].sort()
    else:
        on_edge[i].sort(reverse=True)
total = [item for line in on_edge for item in line]        
st = deque()
st.append(-1)
for val, item in total:
    if st[-1] == item:
        st.pop()
    else:
        st.append(item)
if st[-1] == -1:
    print("YES")
else:
    print("NO")

