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 Ruby (2.3.3) (judge verdict: Accepted)

def l(a,b,r,c)
    ret = 0
    if a == 0
        ret = b
    elsif a == r
        ret = r+2*c-b
    elsif b == c
        ret = c+a
    else
        ret = 2*r+2*c-a
    end
    return ret
end

r,c,n = gets.split.map(&:to_i)
a = Hash.new
b = []
n.times do |i|
    w,x,y,z = gets.split.map(&:to_i)
    if (w == 0 || w == r || x == 0 || x == c) && (y == 0 || y == r || z == 0 || z == c)
        p = l(w,x,r,c)
        q = l(y,z,r,c)
        a[p] = i
        a[q] = i
        b << p << q
    end
end
b.sort!
c = []
b.each do |num|
    if c.empty? || a[c[-1]] != a[num]
        c << num
    else
        c.pop
    end
end
puts (c.empty? ? "YES" : "NO")