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: Wrong Answer)

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

namespace arc076_c
{
	class Program
	{
		static int[] arr;
		static bool IsOK(int index, int key)
		{
			if (arr[index] > key) return true;
			else return false;
		}
		static int Binary_search(int key)
		{
			int ng = -1;
			int ok = arr.Count();

			while (ok - ng > 1)
			{
				int mid = ng + (ok - ng) / 2;

				if (IsOK(mid, key)) ok = mid;
				else ng = mid;
			}

			return ok;
		}
		static void Main(string[] args)
		{
			int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			SortedSet<int> list = new SortedSet<int>();
			bool ret = true;
			for (int i = 0; i < x[2]; i++)
			{
				int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
				if ((a[0] == 0 || a[0] == x[0] || a[1] == 0 || a[1] == x[1]) && (a[2] == 0 || a[2] == x[0] || a[3] == 0 || a[3] == x[1]))
				{
					int n1 = 0;
					if (a[0] == 0) n1 += a[1];//up
					else
					{
						n1 += x[1];
						if (a[1] == x[1]) n1 += a[0];//right
						else
						{
							n1 += x[0];
							if (a[0] == x[0]) n1 += x[1] - a[1];//down
							else//left
							{
								n1 += x[1];
								n1 += x[0] - a[0];
							}
						}
					}
					int n2 = 0;
					if (a[2] == 0) n2 += a[3];//up
					else
					{
						n2 += x[1];
						if (a[3] == x[1]) n2 += a[2];//right
						else
						{
							n2 += x[0];
							if (a[2] == x[0]) n2 += x[1] - a[3];//down
							else//left
							{
								n2 += x[1];
								n2 += x[0] - a[2];
							}
						}
					}
					arr = list.ToArray();
					if (!(Binary_search(n1) == Binary_search(n2) || 
						(Math.Min(n1, n2) < list.Min && list.Max < Math.Max(n1, n2)))) ret = false;
					list.Add(n1); list.Add(n2);
				}
			}
			Console.WriteLine(ret ? "YES" : "NO");
		}
	}
}