Problem:
Score : 700 points

Problem Statement

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.

Sample Input 1

4 2 3
0 1 3 1
1 1 4 1
2 0 2 2

Sample Output 1

YES

The above figure shows a possible solution.

Sample Input 2

2 2 4
0 0 2 2
2 0 0 1
0 2 1 2
1 1 2 1

Sample Output 2

NO

Sample Input 3

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

Sample Output 3

YES

Sample Input 4

1 1 2
0 0 1 1
1 0 0 1

Sample Output 4

NO

Solution in Python (3.4.3) (judge verdict: Accepted)

import sys
from collections import defaultdict

# sys.stdin = open('c1.in')


def read_int_list():
    return list(map(int, input().split()))


def read_int():
    return int(input())


def read_str_list():
    return input().split()


def read_str():
    return input()


def pos(X, Y):
    if Y == 0:
        return X
    if X == r:
        return r + Y
    if Y == c:
        return r + c + r - X
    if X == 0:
        return r + c + r + c - Y


r, c, n, = read_int_list()
x = [0, 0]
y = [0, 0]
a = []
for i in range(n):
    x[0], y[0], x[1], y[1] = read_int_list()
    if (x[0] in [0, r] or y[0] in [0, c]) and (x[1] in [0, r] or y[1] in [0, c]):
        for k in range(2):
            a.append((pos(x[k], y[k]), i))
m = len(a) // 2
a.sort()

res = 'YES'
started = set()
s = []
for p, i in a:
    if i not in started:
        started.add(i)
        s.append(i)
    else:
        if s[-1] != i:
            res = 'NO'
            break
        s.pop()

print(res)