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


class Bit:
    def __init__(self, n):
        self.size = n
        self.tree = [0] * (n + 1)

    def sum(self, i):
        s = 0
        while i > 0:
            s += self.tree[i]
            i -= i & -i
        return s

    def add(self, i, x):
        while i <= self.size:
            self.tree[i] += x
            i += i & -i


def check(x, y):
    if x == 0:
        return y
    elif x == R:
        return R + C + C - y
    elif y == 0:
        return C + R + C + R - x
    elif y == C:
        return C + x
    else:
        return -1


lr_list_raw = []
z_list = []
for i in range(N):
    x1, y1, x2, y2 = map(int, input().split())
    z1, z2 = check(x1, y1), check(x2, y2)
    if z1 >= 0 and z2 >= 0:
        lr_list_raw.append((min(z1, z2), max(z1, z2)))
        z_list.append(z1)
        z_list.append(z2)

z_list.sort()
idx = {zi: i+1 for i, zi in enumerate(z_list)}
lr_list = []
for l_raw, r_raw in lr_list_raw:
    lr_list.append((idx[l_raw], idx[r_raw]))

'''
print(z_list)
print(idx)
print(lr_list_raw)
'''

bit = Bit(max(idx.values()) + 3)
for l, r in lr_list:
    if (bit.sum(r) - bit.sum(l)) % 2 == 1:
        print('NO')
        exit()
    bit.add(l, 1)
    bit.add(r, 1)

print('YES')
