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 main():
    import sys
    input = sys.stdin.readline
    
    R,C,N = map(int,input().split())
    P = []
    X = {0,R}
    Y = {0,C}
    M = 0
    for i in range(N):
        x1,y1,x2,y2 = map(int,input().split())
        if (x1 in X or y1 in Y) and  (x2 in X or y2 in Y):
            if y1==0:
                L1 = x1
            elif x1==R:
                L1 = R+y1
            elif y1==C:
                L1 = 2*R + C - x1
            else:
                L1 = 2*(R+C) - y1
            
            if y2==0:
                L2 = x2
            elif x2==R:
                L2 = R+y2
            elif y2==C:
                L2 = 2*R + C - x2
            else:
                L2 = 2*(R+C) - y2
                
            P.append([min(L1,L2), max(L1,L2)])
    P = sorted(P, key = lambda a:a[0])
    M = len(P)
    
    flag = 0
    Q = []
    for i in range(M):
        x1,x2 = P[i]
        if Q == []:
            Q.append([x1,x2])
        else:
            while Q!=[] and Q[-1][1] < x1:
                Q.pop()
            if Q==[]:
                Q.append([x1,x2])
            else:
                y1,y2 = Q[-1]
                if y2 < x2:
                    flag = 1
                    break
                else:
                    Q.append([x1,x2])
    if flag == 1:
        print("NO")
    else:
        print("YES")
    
main()