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

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

def is_on_edge(x,y):
    return x==0 or x==R or y==0 or y==C

line=[]
for i in range(0,N):
    x1,y1,x2,y2=map(int,input().split())
    if is_on_edge(x1,y1) and is_on_edge(x2,y2):
        line.append([x1,y1,x2,y2])

n=len(line)
query=[]
for i in range(n):
    x1,y1,x2,y2=line[i]
    if y1==0:
        query.append([x1,i])
    elif x1==R:
        query.append([R+y1,i])
    elif y1==C:
        query.append([R+C+(R-x1),i])
    else:
        query.append([2*R+2*C-y1,i])

    if y2==0:
        query.append([x2,i])
    elif x2==R:
        query.append([R+y2,i])
    elif y2==C:
        query.append([R+C+(R-x2),i])
    else:
        query.append([2*R+2*C-y2,i])

query.sort(reverse=True)
que=[]
dic=[0 for i in range(n)]
while query:
    t,num=query.pop()
    if dic[num]==0:
        que.append(num)
        dic[num]=1
    else:
        if que[-1]!=num:
            print("NO")
            exit()
        else:
            dic[num]=2
            que.pop()
print("YES")
