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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
  "bufio"
  "fmt"
  "os"
  "strconv"
  "strings"
)

func main() {
  input := Input{bufio.NewReaderSize(os.Stdin,100)}
  r,c,n := input.Next3Ints()
  h := Pairs{}
  p := Pairs{}
  for i:=0;i<n;i++ {
    x,y,z,w := input.Next4Ints()
    if (x == 0 || x == r || y == 0 || y == c) &&
    (z == 0 || z == r || w == 0 || w == c) {
      h = append(h,Pair{Point{x,y},Point{z,w}})
    } else {
      p = append(p,Pair{Point{x,y},Point{z,w}})
    }
  }
  for i:=0;i<len(h)-1;i++ {
    for j:=i+1;j<len(h);j++ {
      if h[i].Intersec(h[j]) { fmt.Println("NO");return }
    }
  }
  fmt.Println("YES")
}
type Point struct { x,y int }
type Pair struct { p1,p2 Point }
func(p1 Pair) Intersec(p2 Pair) bool {
  ax,ay := p1.p1.x,p1.p1.y
  bx,by := p1.p2.x,p1.p2.y
  cx,cy := p2.p1.x,p2.p1.y
  dx,dy := p2.p2.x,p2.p2.y
  a := (cx-dx)*(ay-cy)+(cy-dy)*(cx-ax)
  b := (cx-dx)*(by-cy)+(cy-dy)*(cx-bx)
  c := (ax-bx)*(cy-ay)+(ay-by)*(ax-cx)
  d := (ax-bx)*(dy-ay)+(ay-by)*(ax-dx)
  return a*b < 0 && c*d < 0
}
type Pairs []Pair

type Input struct { reader *bufio.Reader }
func(i *Input) NextLine() string {
  var buffer []byte
  for {
    line,isPrefix,err := i.reader.ReadLine()
    if err != nil { panic(err) }
    buffer = append(buffer,line...)
    if !isPrefix { break }
  }
  return string(buffer)
}
func(i *Input) Next3Ints() (int,int,int) {
  s := strings.Split(i.NextLine()," ")
  x,_ := strconv.Atoi(s[0])
  y,_ := strconv.Atoi(s[1])
  z,_ := strconv.Atoi(s[2])
  return x,y,z
}
func(i *Input) Next4Ints() (int,int,int,int) {
  s := strings.Split(i.NextLine()," ")
  x,_ := strconv.Atoi(s[0])
  y,_ := strconv.Atoi(s[1])
  z,_ := strconv.Atoi(s[2])
  w,_ := strconv.Atoi(s[3])
  return x,y,z,w
}