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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;

public class Program
{
    private int R, C, N;
    private int[] X1, Y1, X2, Y2, Num1, Num2;

    private Random Rnd;

    public void Solve()
    {
        var sc = new Scanner();
        R = sc.NextInt();
        C = sc.NextInt();
        N = sc.NextInt();
        X1 = new int[N];
        Y1 = new int[N];
        X2 = new int[N];
        Y2 = new int[N];
        for (int i = 0; i < N; i++)
        {
            X1[i] = sc.NextInt();
            Y1[i] = sc.NextInt();
            X2[i] = sc.NextInt();
            Y2[i] = sc.NextInt();
        }

        Num1 = new int[N];
        Num2 = new int[N];
        Rnd = new Random();
        List<int> ls = new List<int>();
        for (int i = 0; i < N; i++)
        {
            bool a = X1[i] == 0 || X1[i] == R || Y1[i] == 0 || Y1[i] == C;
            bool b = X2[i] == 0 || X2[i] == R || Y2[i] == 0 || Y2[i] == C;
            if (a && b)
            {
                ls.Add(i);
                Num1[i] = ToNum(X1[i], Y1[i]);
                Num2[i] = ToNum(X2[i], Y2[i]);
            }
        }

        Console.WriteLine(Check(ls) ? "YES" : "NO");
    }

    private int ToNum(int x, int y)
    {
        // (0,i) = i
        if (x == 0)
        {
            return y;
        }

        // (i, C) = C + i
        if (y == C)
        {
            return C + x;
        }

        // (R,i) = C + R + C-i
        if (x == R)
        {
            return C + R + C - y;
        }

        // (i,0) = C + R + C + R-i
        if (y == 0)
        {
            return C + R + C + R - x;
        }

        return -1;
    }

    private bool Check(List<int> ls)
    {
        if (ls.Count <= 1)
            return true;
        int r = Rnd.Next(ls.Count);

        List<int> aa = new List<int>();

        List<int> bb = new List<int>();

        int max = Math.Max(Num1[ls[r]], Num2[ls[r]]);
        int min = Math.Min(Num1[ls[r]], Num2[ls[r]]);

        foreach (var i in ls)
        {
            if (i == ls[r]) continue;

            bool a = min < Num1[i] && Num1[i] < max;
            bool b = min < Num2[i] && Num2[i] < max;

            if (a ^ b)
                return false;

            if (a)
                aa.Add(i);
            else
                bb.Add(i);
        }

        return Check(aa) && Check(bb);
    }


    public static void Main(string[] args)
    {
        new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);
        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}