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++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<set>
#define ll long long
#define md 1000000007
#define pr(x) cerr<<#x<<"="<<x<<endl;
using namespace std;
int x1,x2,y1,y2,n,m,k,i,tmp,j;
struct node 
{
	int x1,x2,y1,y2;
}a[100010];
bool pan(int x)
{
	if ( (a[x].x1==0||a[x].x1==n)&&(a[x].y1==0||a[x].y1==m)&&(a[x].x2==0||a[x].x2==n)&&(a[x].y2==0||a[x].y2==m) )
	return true;
	else return false;
}
bool cross(int x)
{
	x1=a[i].x1-a[x].x1;
	x2=a[i].x2-a[x].x1;
	y1=a[i].y1-a[x].y1;
	y2=a[i].y2-a[x].y1;
	tmp=x1*y2-x2*y1;
	x1=a[i].x1-a[x].x2;
	x2=a[i].x2-a[x].x2;
	y1=a[i].y1-a[x].y2;
	y2=a[i].y2-a[x].y2;
	if ((x1*y2-x2*y1)*tmp<0) return true;
	return false;
}
int main ()
{
	scanf("%d%d%d",&n,&m,&k);
	for (i=1;i<=k;i++)
	{
		scanf("%d%d%d%d",&a[i].x1,&a[i].y1,&a[i].x2,&a[i].y2);
	}
	for (i=1;i<=k;i++)
	{
		if (pan(i))
		{
			for (j=1;j<=k;i++)
			{
				if (cross(j)) 
				{
					printf("NO\n");
					return 0;
				}
			}
		}
	}
	printf("YES\n");
	return 0;
}