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
from operator import itemgetter
import collections
r,c,n=map(int,input().split())
l=[list(map(int,input().split())) for i in range(n)]
e1=[];e2=[];e3=[];e4=[]
for i in range(n):
  if (l[i][0]==0 or l[i][0]==r or l[i][1]==0 or l[i][1]==c) and (l[i][2]==0 or l[i][2]==r or l[i][3]==0 or l[i][3]==c):
    if l[i][0]==0 and l[i][1]!=c:
      e1.append([i+1,l[i][0],l[i][1]])
    elif l[i][1]==c and l[i][0]!=r:
      e2.append([i+1,l[i][0],l[i][1]])
    elif l[i][0]==r and l[i][1]!=0:
      e3.append([i+1,l[i][0],l[i][1]])
    else:
      e4.append([i+1,l[i][0],l[i][1]])
    if l[i][2]==0 and l[i][3]!=c:
      e1.append([i+1,l[i][2],l[i][3]])
    elif l[i][3]==c and l[i][2]!=r:
      e2.append([i+1,l[i][2],l[i][3]])
    elif l[i][2]==r and l[i][3]!=0:
      e3.append([i+1,l[i][2],l[i][3]])
    else:
      e4.append([i+1,l[i][2],l[i][3]])
e1=sorted(e1,key=itemgetter(2))
e2=sorted(e2,key=itemgetter(1))
e3=sorted(e3,key=itemgetter(2))
e4=sorted(e4,key=itemgetter(1))
e3.reverse()
e4.reverse()
e=e1+e2+e3+e4

q=[]
q=collections.deque(q)
for i in range(len(e)):
  if len(q)==0:
    q.append(e[i][0])
  else:
    if q[-1]==e[i][0]:
      q.pop()
    else:
      q.append(e[i][0])
if len(q)==0:
  print('YES')
else:
  print('NO')