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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#define ll long long
#define rep(i,l,r)for(ll i=(l);i<(r);i++)
#define repp(i,l,r,k)for(ll i=(l);i<(r);i+=(k))

typedef struct piar{ll st,len,i;}P;

ll R,C;
int hikaku(const void*p,const void*q){
	P pp=*(P*)p,qq=*(P*)q;
	if(pp.st<qq.st)return -1;
	if(pp.st>qq.st)return 1;
	if(pp.len<qq.len)return -1;
	if(pp.len>qq.len)return 1;
	return 0;
}

P p[200010];
ll cnt;
void set(int x,int y,int i){
	p[cnt].i=i;
	if(x==0){
		p[cnt].st=0;
		p[cnt].len=y;
	}else if(y==C){
		p[cnt].st=1;
		p[cnt].len=x;
	}else if(x==R){
		p[cnt].st=2;
		p[cnt].len=C-y;
	}else if(y==0){
		p[cnt].st=3;
		p[cnt].len=R-x;
	}
	cnt++;
}
int main(){
	int n;
	scanf("%lld%lld%d",&R,&C,&n);
	rep(i,0,n){
		int a,b,c,d;
		scanf("%d%d%d%d",&a,&b,&c,&d);
		if((a==0||a==R||b==0||b==C)&&(c==0||c==R||d==0||d==C)){
			set(a,b,i);
			set(c,d,i);
		}
	}
	qsort(p,cnt,sizeof(P),hikaku);
	
	int pos=0;
	for(;pos<cnt-1;pos++)if(p[pos].i==p[pos+1].i)break;
	if(pos==cnt-1){
		puts("NO");
		return 0;
	}
	rep(i,0,cnt/2)if(p[(pos-i+cnt)%cnt].i!=p[(pos+1+i)%cnt].i){
		puts("NO");
		return 0;
	}
	puts("YES");
	return 0;
}