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
w, h, n = map(int, input().split())

pos = []
for i in range(n):
    x1, y1, x2, y2 = map(int, input().split())
    if (x1 in [0, w] or y1 in [0, h]) and (x2 in [0, w] or y2 in [0, h]):
        pos.append((x1, y1, i))
        pos.append((x2, y2, i))

pos.sort(key=lambda v: v[0]) # top →
edge = [v[-1] for v in pos if v[1] == 0 and v[0] != 0]

pos.sort(key=lambda v: v[1]) # left ↓
edge += [v[-1] for v in pos if v[0] == w and v[1] != 0]

pos.sort(key=lambda v: v[0], reverse=True) # bottom ←
edge += [v[-1] for v in pos if v[1] == h and v[0] != w]

pos.sort(key=lambda v: v[1], reverse=True) # right ↑
edge += [v[-1] for v in pos if v[0] == 0 and v[1] != h]

# for i in range(len(edge) - 1):
#     if edge[i] == edge[i + 1]:
#         break
# for j in range(len(edge) // 2):
#     if edge[(i + j + 1) % n] != edge[(i - j + n) % n]:
#         print("NO")
#         break
# else:
#     print("YES")

# print(edge)
hist = [None] * n
step = 0
for v in edge:
    if hist[v] is None:
        hist[v] = step + 1
        step += 1
    else:
        if hist[v] != step:
            print("NO")
            break
        step -= 1
else:
    print("YES")

