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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int r,c,n;
set<pair<int,int> > st;
int dis(int x,int y){
	if(x==0) return y;
	if(y==c) return y+x;
	if(x==r) return r+c+c-y;
	if(y==0) return c+c+r+r-x;
	return -1;
}
int main(){
	scanf("%d%d%d",&r,&c,&n);
	for(int i=1;i<=n;i++){
		int x1,y1,x2,y2,d1,d2;
		scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
		d1=dis(x1,y1);
		d2=dis(x2,y2);
		if(d1!=-1&&d2!=-1) st.insert(make_pair(min(d1,d2),max(d1,d2)));
	}
	int mx=0;
	for(auto x=st.begin();x!=st.end();x++){
		if(x->first >= mx) mx=x->second;
		else if(x->second > mx) return puts("NO"),0;
	}
	return puts("YES"),0;
}