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 <cstdio>
#include <cstring>
#include <vector>
#include <queue>
#include <string>
#include <algorithm>
#include <iostream>
#include <string>
#include <map>
#include <set>
#include <functional>
#include <iostream>
#define MOD 1000000007LL
using namespace std;
typedef long long ll;
typedef pair<int,int> P;

int r,c,n;
bool flag[2];
P p[2];
vector<int> xt;
vector<int> xd;
vector<int> yt;
vector<int> yd;

int main(void){
	scanf("%d%d%d",&r,&c,&n);
	bool res=true;
	for(int i=0;i<n;i++){
		scanf("%d%d",&p[0].first,&p[0].second);
		scanf("%d%d",&p[1].first,&p[1].second);
		if(abs(p[0].first-p[1].first)==r){
			if(abs(p[0].second-p[1].second)==c){
				if(p[0].second>p[1].second)swap(p[0],p[1]);
				if(flag[0] || flag[1])res=false;
				flag[0]=true;
				flag[1]=true;
			}else{
				if(flag[1])res=false;
				flag[0]=true;
			}
		}else if(abs(p[0].second-p[1].second)==c){
			if(flag[0])res=false;
			flag[1]=true;
		}
	}
	printf("%s\n",res?"YES":"NO");
	return 0;
}