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 <iostream>
#include <string.h>
#include <algorithm>
#include <vector>
#include <stack>

#define pb push_back
#define mp make_pair
#define ll long long
#define ull unsigned ll
#define db double
#define INF 0x3f3f3f3f
#define MOD 1000000007
#define PII pair<int, int>
 
using namespace std;

int r,c,n;
int x1,x2,y1,y2;
bool vis[100005];

inline bool border(int x,int y) {
	return x==0 || x==r || y==0 || y==c;
}

struct node {
	int val,side,pos;
	bool operator<(const node& rhs) const {
		if (side!=rhs.side) return side<rhs.side;
		if (side==1||side==2) return pos<rhs.pos;
		else return pos>rhs.pos;	
	}
};

vector<node> vec;
void add(int x,int y,int idx) {
	if (x==0) vec.pb({idx,1,y});
	else if (x==r) vec.pb({idx,3,y});
	else if (y==0) vec.pb({idx,2,x});
	else vec.pb({idx,4,x});
}

int main() {
	scanf("%d%d%d",&r,&c,&n);
	for (int i=0;i<n;i++) {
		scanf("%d%d%d%d",&x1,&y1,&x2,&y2);
		if (border(x1,y1)&&border(x2,y2)) {
			add(x1,y1,i);
			add(x2,y2,i);
		}
	}
	sort(vec.begin(),vec.end());
	bool flag=true;
	stack<int> st;
	for (int i=0;i<vec.size();i++) {
		if (!vis[vec[i].val]) {
			vis[vec[i].val]=1;
			st.push(vec[i].val);
		} else {
			if (vec[i].val!=st.top()) {
				flag=false;
				break;
			} else {
				st.pop();
			}
		}
	}
	if (flag) printf("YES\n");
	else printf("NO\n");
}