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<bits/stdc++.h>
#define range(i,a,b) for(int i = (a); i < (b); i++)
#define rep(i,b) for(int i = 0; i < (b); i++)
#define all(a) (a).begin(), (a).end()
#define show(x)  cerr << #x << " = " << (x) << endl;
//const int INF = 1e8;
using namespace std;

int r, c, n;
map<int,char> up,rt,lt,dn;
char w = 'a';

bool C(int a, int b){
	if( (a == 0 || a == r) || (b == 0 || b == c) ) return true;
	return false;
}

bool isEdge(int a, int b, int c, int d){
	return C(a,b) && C(c,d);
}

void addVector(int a, int b){
	if(a == 0) up[b] = w;
	else if(b == c) rt[a] = w;
	else if(a == r) lt[-b] = w;
	else if(b == 0) dn[-a] = w;
}

int main(){
	cin >> r >> c >> n;

	rep(i,n){
		int a, b, c, d;
		cin >> a >> b >> c >> d;
		if(isEdge(a,b,c,d)){
			addVector(a,b);
			addVector(c,d);
			w++;
		}
	}

	vector<char> al;
	for(auto i : up) al.emplace_back(i.second);
	for(auto i : rt) al.emplace_back(i.second);
	for(auto i : lt) al.emplace_back(i.second);
	for(auto i : dn) al.emplace_back(i.second);

	vector<char> ans;
	rep(i,al.size()){
		//show(al[i])
		if(ans.empty()) ans.emplace_back(al[i]);
		else{
			if(al[i] == ans.back()){
				ans.pop_back();
			}else{
				ans.emplace_back(al[i]);
			}
		}
	}
	if(ans.size() == 0) cout << "YES" << endl;
	else cout << "NO" << endl;
}