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>
#include <string.h>
#include <math.h>
#define swap(type,a,b) do{type t=a;a=b;b=t;}while(0);
#define MAX(a,b) (((a)>(b))?(a):(b))
#define MIN(a,b) (((a)<(b))?(a):(b))
#define ll long long
#define INF 100000000
#define FOR(i,a,n) for(i=a;i<n;i++)
void fill(int a[],int b,int c){
	int i;
	FOR(i,0,b) a[i]=c;
	return;
}
typedef struct{
	int a,b;
}Line;
int comp(const void* a,const void* b){
	return ((Line*)a)->a - ((Line*)b)->a;
}
Line line1[100000],line2[100000];
int main(void)
{
	int r,c,n,dx,dy,i;
	int s1=0,s2=0,h=0,w=0;
	int X1,Y1,X2,Y2;
	scanf("%d%d%d",&r,&c,&n);
	FOR(i,0,n){
		scanf("%d%d%d%d",&X1,&Y1,&X2,&Y2);
		if(X1>X2) swap(int,X1,X2);
		if(Y1>Y2) swap(int,Y1,Y2);
		dx=X2-X1;
		dy=Y2-Y1;
		if(dx==r||dy==c){
			if(h||w){
				puts("NO");
				return 0;
			}
			h=w=1;
			line1[s1].a=X1,line1[s1++].b=X2;
			line2[s2].a=Y1,line2[s2++].b=Y2;
		}
		else if(dx==r){
			if(h){
				puts("NO");
				return 0;
			}
			w=1;
			line2[s2].a=Y1,line2[s2++].b=Y2;
		}
		else if(dy==c){
			if(w){
				puts("NO");
				return 0;
			}
			h=1;
			line1[s1].a=X1,line1[s1++].b=X1;
		}
	}
	if(s1==0&&s2==0){
		puts("YES");
		return 0;
	}
	qsort(line1,s1,sizeof(Line),comp);
	FOR(i,0,s1-1){
		if(line1[i].b>line1[i+1].b){
			puts("NO");
			return 0;
		}
	}
	qsort(line2,s2,sizeof(Line),comp);
	FOR(i,0,s2-1){
		if(line2[i].b>line2[i+1].b){
			puts("NO");
			return 0;
		}
	}
	puts("YES");
	return 0;
}