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>
#define ll long long
using namespace std;
const int maxn=100005;
inline int read(){
	int u=0,f=1;char c=getchar();
	while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
	while(c>='0'&&c<='9'){u=u*10+c-'0';c=getchar();}
	return u*f;
}

int r,c;
struct P{
	int pos,x;
}p[4][maxn];
int cnt[4];
int is_bod(int x,int y){
	if(x==0)return 0;
	if(y==c)return 1;
	if(x==r)return 2;
	if(y==0)return 3;
	return -1; 
}
bool cmp1(P x,P y){
	return x.pos<y.pos;
}
bool cmp2(P x,P y){
	return x.pos>y.pos;
}
int sta[maxn];
int top=0,n;
int main(){
	r=read();c=read();n=read();
	for(int i=1;i<=n;i++){
		int x1=read(),y1=read(),x2=read(),y2=read();
		int f1=is_bod(x1,y1),f2=is_bod(x2,y2);
	//	if(x1==r||x1)
		if((x1%r)&&(y1%c)||(x2%r)&&(y2%c))continue;
		
		cnt[f1]++;cnt[f2]++;
		p[f1][cnt[f1]].pos=(f1%2==0?y1:x1);
		p[f1][cnt[f1]].x=i;
		p[f2][cnt[f2]].pos=(f2%2==0?y2:x2);
		p[f2][cnt[f2]].x=i;
		
	}
	for(int i=0;i<4;i++){
		if(i<2)sort(p[i]+1,p[i]+cnt[i]+1,cmp1);
		else sort(p[i]+1,p[i]+cnt[i]+1,cmp2);
		for(int j=1;j<=cnt[i];j++){
			if(sta[top]==p[i][j].x&&top)top--;
			else top++,sta[top]=p[i][j].x;
		}
	}
	if(top!=0)puts("NO");
	else puts("YES");
	return 0;
}