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
def calc_pos(x, y, R, C):
    if y == 0:
        return x
    if y == C:
        return 2 * R + C - x
    if x == R:
        return R + y
    if x == 0:
        return 2 * R + 2 * C - y

def read_data():
    R, C, N = map(int, input().split())
    pairs = []
    xys = []
    idx = 0
    for i in range(N):
        x1, y1, x2, y2 = map(int, input().split())
        xys.append((x1, y1))
        xys.append((x2, y2))
        if (x1 != 0 and x1 != R and y1 != 0 and y1 != C) or (x2 != 0 and x2 != R and y2 != 0 and y2 != C):
            continue
        a = calc_pos(x1, y1, R, C)
        b = calc_pos(x2, y2, R, C)
        pairs.append((a, idx))
        pairs.append((b, idx))
        idx += 1
    pairs.sort()
    return pairs, xys

def is_valid(xys):
    xys.sort()
    prev_x, prev_y = xys[0]
    for x, y in xys[1:]:
        if prev_x == x and prev_y == y:
            return False
        prev_x = x
        prev_y = y
    return True

def solve(pairs, xys):
    if len(xys) == 2:
        return "YES"
    if not is_valid(xys):
        return "NO"    
    idxs = [i for a, i in pairs]
    stack = []
    for idx in idxs:
        if stack and stack[-1] == idx:
            stack.pop()
            continue
        stack.append(idx)
    if stack:
        return "NO"
    else:
        return "YES"

pairs, xys = read_data()
print(solve(pairs, xys))
