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 operator import itemgetter

X, Y, N = map(int, input().split())
U = []
D = []
R = []
L = []

def mustconsider(x, y):
    return (x in [0, X]) or (y in [0, Y])

def divide(x, y, i):
    if x == 0 and y != Y:
        L.append((y, i))
    if x == X and y != 0:
        R.append((y, i))
    if y == 0 and x != 0:
        D.append((x, i))
    if y == Y and x != X:
        U.append((x, i))

for i in range(N):
    x1, y1, x2, y2 = map(int, input().split())
    if mustconsider(x1, y1) and mustconsider(x2, y2):
        divide(x1, y1, i)
        divide(x2, y2, i)

D.sort()
R.sort()
U.sort(reverse=True)
L.sort(reverse=True)

Arounds = []
for _, ind in D:
    Arounds.append(ind)
for _, ind in R:
    Arounds.append(ind)
for _, ind in U:
    Arounds.append(ind)
for _, ind in L:
    Arounds.append(ind)

stack = []
for a in Arounds:
    if not stack:
        stack.append(a)
    else:
        if stack[-1] == a:
            stack.pop()
        else:
            stack.append(a)

print("YES" if not stack else "NO")