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
#!/usr/bin/env python3


def add(bound, r, c, x, y, i):
    if x == 0:
        bound.append((0, y, i))
    elif y == c:
        bound.append((1, x, i))
    elif x == r:
        bound.append((2, c - y, i))
    else:
        bound.append((3, r - x, i))


def solve(bound):

    if not bound:
        return True

    bound.sort()
    st = [0] * len(bound)
    p = -1

    for _, _, i in bound:
        if 0 <= p and st[p] == i:
            p -= 1
        else:
            p += 1
            st[p] = i

    return p == -1


def main():
    r, c, n = input().split()
    r = int(r)
    c = int(c)
    n = int(n)
    bound = []
    for i in range(n):
        x1, y1, x2, y2 = input().split()
        x1 = int(x1)
        y1 = int(y1)
        x2 = int(x2)
        y2 = int(y2)
        if (x1 % r == 0 or y1 % c == 0) and (x2 % r == 0 or y2 % c == 0):
            add(bound, r, c, x1, y1, i)
            add(bound, r, c, x2, y2, i)


    print('YES' if solve(bound) else 'NO')


if __name__ == '__main__':
    main()

