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>
using namespace std;

int w,h,n;
struct td{
    int x,y,i;
    td() {}
    td(int x,int y,int i):x(x),y(y),i(i) {}
    
    bool lower() const {return y==0 || x==w; }
    bool operator<(const td &rhs)const {
        if(lower()) {
            if(rhs.lower()) return x+y<rhs.x+rhs.y;
            else return true;
        } else {
            if(rhs.lower()) return false;
            else return x+y>rhs.x+rhs.y;
        }
    }
};

vector<td> arr;

bool side(int p,int v) {
    return p==0 || p==v;
}
int main() {
    scanf("%d%d%d",&w,&h,&n);
    for(int i=1;i<=n;i++) {
        int a,b,c,d;
        scanf("%d%d%d%d",&a,&b,&c,&d);
        if((side(a,w) || side(b,h)) && (side(c,w) || side(d,h))) {
            td q(a,b,i), w(c,d,i);
            if(w<q) swap(q,w);
            w.i=-w.i;
            arr.push_back(q);
            arr.push_back(w);
        }
    }

    sort(arr.begin(),arr.end());
    
    stack<int> stk;
    for(auto &v:arr) {
        if(v.i>0) stk.push(v.i);
        else {
            if(-v.i!=stk.top()) {
                puts("NO");
                return 0;
            }
            stk.pop();
        }
    }
    puts("YES");
    
    return 0;
}