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 hantei(x,y):

    if y == 0:
        return "l"
    elif x == R:
        return "d"
    elif y == C:
        return "r"
    elif x == 0:
        return "u"

    return "n"

R,C,N = map(int,input().split())

u = []
l = []
d = []
r = []

for i in range(N):

    X1,Y1,X2,Y2 = map(int,input().split())

    if hantei(X1,Y1) != "n" and hantei(X2,Y2) != "n":


        if hantei(X1,Y1) == "l":
            l.append([X1,Y1,i])
        elif hantei(X1,Y1) == "d":
            d.append([X1,Y1,i])
        elif hantei(X1,Y1) == "r":
            r.append([X1,Y1,i])
        elif hantei(X1,Y1) == "u":
            u.append([X1,Y1,i])

        X1 = X2
        Y1 = Y2
    
        if hantei(X1,Y1) == "l":
            l.append([X1,Y1,i])
        elif hantei(X1,Y1) == "d":
            d.append([X1,Y1,i])
        elif hantei(X1,Y1) == "r":
            r.append([X1,Y1,i])
        elif hantei(X1,Y1) == "u":
            u.append([X1,Y1,i])

l.sort()
d.sort()
r.sort()
r.reverse()
u.sort()
u.reverse()

ps = []
for i in l:
    ps.append(i[2])
for i in d:
    ps.append(i[2])
for i in r:
    ps.append(i[2])
for i in u:
    ps.append(i[2])

q = []

for i in ps:
    if len(q) > 0 and q[-1] == i:
        del q[-1]
    else:
        q.append(i)

if len(q) == 0:
    print ("YES")
else:
    print ("NO")

