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
import sys
input = sys.stdin.readline

def main():
    R, C, N = map(int, input().split())
    xyxy = [list(map(int, input().split())) for i in range(N)]

    r = []

    for i in range(N):
        x1, y1, x2, y2 = xyxy[i]
        # どちらも周上にある場合は周上の座標に変換してから記録
        if ((x1 == 0 or x1 == R) or (y1 == 0 or y1 == C)) and ((x2 == 0 or x2 == R) or (y2 == 0 or y2 == C)):
            # １つ目
            if x1 == 0:
                r.append((y1, i))
            elif x1 == R:
                r.append((C - y1 + C + R, i))
            elif y1 == 0:
                r.append((R - x1 + C * 2 + R, i))
            else:
                r.append((x1 + C, i))
            # 2つ目
            if x2 == 0:
                r.append((y2, i))
            elif x2 == R:
                r.append((C - y2 + C + R, i))
            elif y2 == 0:
                r.append((R - x2 + C * 2 + R, i))
            else:
                r.append((x2 + C, i))
    
    r = sorted(r)
    # print(r)
    stack = []
    for i in range(len(r)):
        if len(stack) > 0:
            if stack[-1] == r[i][1]:
                stack.pop()
            else:
                stack.append(r[i][1])
        else:
            stack.append(r[i][1])
    
    if len(stack) > 0:
        print("NO")
    else:
        print("YES")
            



if __name__ == "__main__":
    main()