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)

r, c, n = gets.split.map(&:to_i)
bd = [0, r, c]
xy = n.times.map { |i|
  gets.split.map(&:to_i) + [i]
}.select{ |x1, y1, x2, y2, id|
  (bd.include?(x1) || bd.include?(y1)) &&
    (bd.include?(x2) || bd.include?(y2))
}

ea, eb, ec, ed = [], [], [], []

xy.each{ |x1, y1, x2, y2, id|
  [[x1, y1], [x2, y2]].each{ |x, y|
    t = [x, y, id]
    if x == 0
      ea << t
    elsif y == c
      eb << t
    elsif x == r
      ec << t
    else
      ed << t
    end
  }
}

ea.sort_by!{ |x| x[1] }
eb.sort_by!{ |x| x[0] }
ec.sort_by!{ |x| -x[1] }
ed.sort_by!{ |x| -x[0] }

st = ea + eb + ec + ed
q = []
st.each{ |x, y, id| q[-1] == id ? q.pop : q << id }
puts q.size.zero? ? :YES : :NO