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)
left, right, top, bottom = [], [], [], []
(1..N).each do |i|
    x1, y1, x2, y2 = gets.split.map(&:to_i)
    arrs = [[x1, y1], [x2, y2]]
    next unless arrs.all?{|x, y|
        x == 0 || x == R || y == 0 || y == C
    }
    [[x1, y1], [x2, y2]].each do |x, y|
        if x == 0
            top.push([i, y])
        elsif x == R
            bottom.push([i, y])
        elsif y == 0
            left.push([i, x])
        elsif y == C
            right.push([i, x])
        end
    end
end

order = top.sort_by{|arr|arr[1]}.map{|arr|arr[0]}
order.concat(right.sort_by{|arr|arr[1]}.map{|arr|arr[0]})
order.concat(bottom.sort_by{|arr|-arr[1]}.map{|arr|arr[0]})
order.concat(left.sort_by{|arr|-arr[1]}.map{|arr|arr[0]})

while order.length > 0
    if order[0] == order[1]
        order.shift(2)
    elsif order[0] == order[-1]
        order.shift
        order.pop
    else
        puts 'NO'
        exit
    end
end
puts 'YES'