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
from collections import deque
R,C,N=map(int,input().split())
table=[]
def f(i,j):
    if i==0:
        return j
    if j==C:
        return C+i
    if i==R:
        return R+C+C-j
    if j==0:
        return R+R+C+C-i
for i in range(N):
    a,b,c,d=map(int,input().split())
    if (0<a<R and 0<b<C) or (0<c<R and 0<d<C):
        continue
    table.append((f(a,b),i))
    table.append((f(c, d), i))
table.sort()
H=deque()
for i in range(len(table)):
    if len(H)!=0 and H[-1]==table[i][1]:
        H.pop()
    else:
        H.append(table[i][1])
#print(H,table)
while len(H)!=0 and H[0]==H[-1]:
    H.popleft()
    H.pop()
if len(H)==0:
    print('YES')
else:
    print('NO')