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;

namespace arc076_c
{
	class Program
	{
		static int[] x;
		static bool onedge(int a, int b)
		{
			if (a == 0 || a == x[0]) return true;
			if (b == 0 || b == x[1]) return true;
			return false;
		}
		static int howlong(int a, int b)
		{
			if (a == 0) return b;//up
			if (b == x[1]) return x[1] + a;//right
			if (a == x[0]) return x[1] + x[0] + (x[1] - b);//down
			else return x[1] + x[0] + x[1] + (x[0] - a);//left
		}
		static void Main(string[] args)
		{
			x = Console.ReadLine().Split().Select(int.Parse).ToArray();
			List<Tuple<int, int>> list = new List<Tuple<int, int>>();
			for (int i = 0; i < x[2]; i++)
			{
				int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
				if (onedge(a[0], a[1]) && onedge(a[2], a[3]))
				{
					int n1 = howlong(a[0], a[1]); list.Add(new Tuple<int, int>(n1, i));
					int n2 = howlong(a[2], a[3]); list.Add(new Tuple<int, int>(n2, i));
				}
			}
			Tuple<int, int>[] arr = list.ToArray();
			Array.Sort(arr);
			Stack<int> stack = new Stack<int>();
			foreach (var tup in arr)
			{
				if (stack.Count == 0) stack.Push(tup.Item2);
				else if (stack.Peek() == tup.Item2) stack.Pop();
				else stack.Push(tup.Item2);
			}
			Console.WriteLine(stack.Count == 0 ? "YES" : "NO");
		}
	}
}