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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int R = sc.nextInt();
    int C = sc.nextInt();
    int N = sc.nextInt();
    ArrayList<Vertice> alist = new ArrayList<Vertice>();
    ArrayList<Vertice> blist = new ArrayList<Vertice>();
    ArrayList<Vertice> clist = new ArrayList<Vertice>();
    ArrayList<Vertice> dlist = new ArrayList<Vertice>();
    for(int i = 0; i < N; i++) {
      int x1 = sc.nextInt();
      int y1 = sc.nextInt();
      int x2 = sc.nextInt();
      int y2 = sc.nextInt();
      if(((x1 == 0) || (x1 == R) || (y1 == 0) || (y1 == C)) && ((x2 == 0) || (x2 == R) || (y2 == 0) || (y2 == C))) {
        Vertice v1 = new Vertice(i, x1, y1);
        Vertice v2 = new Vertice(i, x2, y2);
        if((x1 == 0) && (y1 < C)) alist.add(v1);
        if((x1 < R) && (y1 == C)) blist.add(v1);
        if((x1 == R) && (y1 > 0)) clist.add(v1);
        if((x1 > 0) && (y1 == 0)) dlist.add(v1);

        if((x2 == 0) && (y2 < C)) alist.add(v2);
        if((x2 < R) && (y2 == C)) blist.add(v2);
        if((x2 == R) && (y2 > 0)) clist.add(v2);
        if((x2 > 0) && (y2 == 0)) dlist.add(v2);
      }
    }
    Collections.sort(alist, new Comparator<Vertice>() {
      public int compare(Vertice vertice1, Vertice vertice2) {
	return vertice1.y - vertice2.y;
      }
    });
    Collections.sort(blist, new Comparator<Vertice>() {
      public int compare(Vertice vertice1, Vertice vertice2) {
	return vertice1.x - vertice2.x;
      }
    });
    Collections.sort(clist, new Comparator<Vertice>() {
      public int compare(Vertice vertice1, Vertice vertice2) {
	return vertice2.y - vertice1.y;
      }
    });
    Collections.sort(dlist, new Comparator<Vertice>() {
      public int compare(Vertice vertice1, Vertice vertice2) {
	return vertice2.x - vertice1.x;
      }
    });
    String ans = "YES";
    Stack<Integer> st = new Stack<Integer>();
    int[] count = new int[N];
    for(int i = 0; i < alist.size(); i++) {
      Vertice v = alist.get(i);
      if(count[v.id] == 0) {
        st.push(v.id);
        count[v.id]++;
      } else {
        int p = st.pop();
        if(v.id != p) {
          ans = "NO";
          break;
        }
      }
    }

    for(int i = 0; i < blist.size(); i++) {
      Vertice v = blist.get(i);
      if(count[v.id] == 0) {
        st.push(v.id);
        count[v.id]++;
      } else {
        int p = st.pop();
        if(v.id != p) {
          ans = "NO";
          break;
        }
      }
    }

    for(int i = 0; i < clist.size(); i++) {
      Vertice v = clist.get(i);
      if(count[v.id] == 0) {
        st.push(v.id);
        count[v.id]++;
      } else {
        int p = st.pop();
        if(v.id != p) {
          ans = "NO";
          break;
        }
      }
    }

    for(int i = 0; i < dlist.size(); i++) {
      Vertice v = dlist.get(i);
      if(count[v.id] == 0) {
        st.push(v.id);
        count[v.id]++;
      } else {
        int p = st.pop();
        if(v.id != p) {
          ans = "NO";
          break;
        }
      }
    }
    
    System.out.println(ans);    
  }

  static class Vertice {
    int id;
    int x;
    int y;
  
    public Vertice(int id, int x, int y) {
      this.id = id;
      this.x = x;
      this.y = y;
    }
  }
}