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 pb push_back
typedef long long ll;
using namespace std;
ll R , C , N;
class curv
{
public:
        ll x , y , z , w , id;
        curv()
        {

        }
        curv(ll a , ll b , ll c , ll d , ll u)
        {
                x = a;
                y = b;
                z = c;
                w = d;
                id = u;
        }
};
vector<curv> pts;
bool corner(ll a , ll b)
{
        if(a == 0 || a == R) return true;
        if(b == 0 || b == C) return true;
        return false;
}
bool special(ll a , ll b , ll c , ll d)
{
        return (corner(a , b) && corner(c , d));
}
vector< pair< ll, ll> > XX;
int main()
{
        cin >> R >> C >> N;
        for(ll i = 1 ; i<=N;i++)
        {
                ll a , b , c , d;
                cin >> a>> b >> c >> d;
                if(special(a ,b,c,d)) {
                        curv X(a,b,c,d , i);
                        pts.pb(X);
                }
        }
        ll off = (R+C)*3;
        for(auto i : pts)
        {
                if(i.y == 0 || i.x == R) {
                        XX.pb(make_pair(i.x+i.y , i.id));
                }else{
                        XX.pb(make_pair(off - i.x - i.y , i.id));
                }

                if(i.w == 0 || i.z == R) {
                        XX.pb(make_pair(i.z+i.w , i.id));
                }else{
                        XX.pb(make_pair(off - i.z - i.w , i.id));
                }
        }
        sort(XX.begin() , XX.end());
        stack< ll> S;
        for(auto i : XX)
        {
                if(S.empty())
                {
                        S.push(i.second); continue;
                }else{
                        ll u = S.top();
                        if(u == i.second) {
                                S.pop();
                        }else{
                                S.push(i.second);
                        }
                }
        }
        S.empty() ? cout << "YES\n" : cout << "NO\n";
        return 0;
}