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 <stdio.h>
#include <algorithm>
#include <iostream>
#include <memory.h>
#include <queue>

using namespace std;
const int maxn = 200005;
int r,c,n,tot,stk[maxn],top,ins[maxn];
struct node {int x,y,i,l;}p[maxn];
int ask(int x,int y) {
	if (x==0) return 1;
	if (y==c) return 2;
	if (x==r) return 3;
	if (y==0) return 4;
	return 0;
}
bool comp(node a,node b) {
	if (a.l!=b.l) return a.l<b.l;
	if (a.l==1) return a.y<b.y;
	if (a.l==2) return a.x<b.x;
	if (a.l==3) return a.y>b.y;
	return a.x>b.x;
}

int main()
{
	#ifndef ONLINE_JUDGE
		freopen("connected.in","r",stdin);
		freopen("connected.out","w",stdout);
	#endif
	scanf("%d %d %d",&r,&c,&n);
	for (int i=1;i<=n;i++)
	{
		int x1,y1,l1;scanf("%d %d",&x1,&y1);l1=ask(x1,y1);
		int x2,y2,l2;scanf("%d %d",&x2,&y2);l2=ask(x2,y2);
		if (l1&&l2)
			p[++tot]=(node){x1,y1,i,l1},
			p[++tot]=(node){x2,y2,i,l2};
	}
	sort(p+1,p+tot+1,comp);
	for (int v,i=1;i<=tot;i++)
	if (!ins[v=p[i].i]) stk[++top]=v,ins[v]=1;
	else {
		if (stk[top]!=v) {puts("NO");return 0;}
		top--;
	}
	puts("YES");
	return 0;
}