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<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int lim=200000000;
struct data{
	int v,n;
}a[210001];
int i,j,k,n,r,c,m,t1,t2,t3,t4,flag,b[210001],q[210001];
bool cmp(data a,data b){
	return a.v<b.v;
}
int calc(int x,int y){
	if (!y) return 1+x;
	if (x==r) return lim+y;
	if (y==c) return 2*lim+r-x;
	if (!x) return 3*lim+c-y;
	return 0;
}
int main(){
	scanf("%d%d%d",&r,&c,&n);memset(b,0,sizeof(b));
	for (i=1,m=0;i<=n;i++){
		scanf("%d%d%d%d",&t1,&t2,&t3,&t4);
		j=calc(t1,t2);k=calc(t3,t4);
		if (!j||!k) continue;
		a[++m].v=j;a[m].n=i;a[++m].v=k;a[m].n=i;
	}
	if (m) sort(a+1,a+1+m,cmp);
	for (q[0]=0,i=flag=1;i<=m;i++){
		if (!b[a[i].n]){
			b[a[i].n]=1;q[++q[0]]=a[i].n;
		}else{
			if (q[q[0]]!=a[i].n){
				flag=0;break;
			}
			q[0]--;
		}
	}
	puts(flag?"YES":"NO");
	return 0;
}