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: Accepted)

#include<bits/stdc++.h>
#define For(i,a,b) for(int i=a;i<=b;i++)
#define MOD 1000000007
#define pb push_back
#define Long long long 
using namespace std;
stack<int> S;
	int R,C,N,a,b,c,d;
bool isBound(int x, int y){
	if((x==0 || x == C) || (y==0 || y == R) )  return true;
	return false;
}
typedef pair<int,int> ii;
vector<ii> v;
int count(int x, int y){
	int c = C+1;
	int r = R+1;	
	if(y==0) return x;
	if(x==C) return c+y;	
	if(y==R) return r+c+(c-x);
//	cout << "return  " << c+r+c+r-y;
	if(x==0) return c+r+c+r-y;		
}

main(){
	cin >> R >> C >> N;
	For(i,1,N){
		scanf("%d%d",&b,&a);		
		scanf("%d%d",&d,&c);
		if(isBound(a,b) && isBound(c,d)){
//			cout << "push " << count(a,b) << " . " << a << " " << b << endl;
//			cout << "push " << count(c,d) << " . " << c << " " << d << endl;
			v.pb(ii(count(a,b),i));
			v.pb(ii(count(c,d),i));
		}
	}
	sort(v.begin(),v.end());		
	for(int i=0;i<v.size();i++){
//		cout << v[i] << " " ;
		if(S.empty()){
			S.push(v[i].second);
		}	else	if(S.top()==v[i].second){
			S.pop();
		}	else	{
			S.push(v[i].second);
		}
	}
	if(S.empty()){
		cout << "YES";
	}	else	{
		cout << "NO";
	}
}