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: Wrong Answer)

R,C,N = gets.split.map(&:to_i)
RR = R+1; CC = C+1
pts = []

def onedge(x,y)
  case
  when y == 0
    x
  when x == C
    C + y
  when y == R
    C + R + C - x
  when x == 0
    C + R + C + R - y
  else
    nil
  end
end

N.times{ |i|
  x1,y1,x2,y2 = gets.split.map(&:to_i)
  r1 = onedge(x1,y1); r2 = onedge(x2,y2)
  if r1 && r2
    #p "#{x1},#{y1} -> #{r1} / #{x2},#{y2} -> #{r2}"
    pts << [r1,i]; pts << [r2,i]
  end
}

#p pts
pts.sort!
#p pts

stack = []
sh = {}
pts.map{ |r,i|
  if sh[i]
    if stack[-1] == i
      stack.pop
      sh.delete(i)
    else
      puts "NO"
      exit
    end
  else
    stack << i
    sh[i] = 1
  end
}

puts "YES"