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
# coding: utf-8
# Your code here!

import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意


r,c,n = [int(i) for i in readline().split()]
#xyxy = [[int(i) for i in readline().split()] for _ in range(n)] 
#for i,(x1,y1,x2,y2) in enumerate(xyxy):

def addedge(x1,y1):
    if   y1 == 0:
        edge.append((x1,i))
    elif x1 == r:
        edge.append((r+y1,i))
    elif y1 == c:
        edge.append((r+c+(r-x1),i))
    else:
        edge.append((r+c+r+(c-y1),i))
    return 


edge = []
for i in range(n):
    x1,y1,x2,y2 = [int(i) for i in readline().split()]
    if (x1 not in (0,r) and y1 not in (0,c)) or (x2 not in (0,r) and y2 not in (0,c)):
        continue
    
    addedge(x1,y1)
    addedge(x2,y2)

        
edge.sort()
#print(edge)

ans = []
for d,i in edge:
    if ans and ans[-1] == i:
        ans.pop()
    else:
        ans.append(i)

if ans:
    print("NO")
else:
    print("YES")
    


    




