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 Scala (2.13.1) (judge verdict: Wrong Answer)

import scala.collection.mutable._

object Main extends App {
  val Array(r, c, n) = io.StdIn.readLine.split(" ").map(_.toInt)
  
  val lines = 1.to(n).map { _ => io.StdIn.readLine.split(" ").map(_.toInt) }
  
  val yes = lines.zipWithIndex.forall {
      case (Array(x1, y1, x2, y2), i) =>
      val isSplit =
        (x1 == 0 || x1 == r) &&
        (y1 == 0 || y1 == c) &&
        (x2 == 0 || x2 == r) &&
        (y2 == 0 || y2 == c)
    
     if (isSplit) {
       val (minX, maxX) = if (x1 < x2) (x1, x2) else (x2, x1)
       val (minY, maxY) = if (y1 < y2) (y1, y2) else (y2, y1)
       lines.take(i).forall {
         case Array(x3, y3, x4, y4) =>
           val isFailure = 
             minX <= x3 && x3 <= maxX &&
             minX <= x4 && x4 <= maxX &&
             minY <= y3 && y3 <= maxY &&
             minY <= y4 && y4 <= maxY
           !isFailure
       }
     } else {
       true
     }
  }
  
  println(if (yes) "YES" else "NO")
}