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 <bits/stdc++.h>
#define mk make_pair
#define fs first
#define sc second
using namespace std;
typedef long long ll;
typedef long double ld;
vector<pair<long long, int>> a;
int main(){
  int n, r, c, x, y, v, b;
  long long tmp;
  while(cin>>r>>c>>n){
    a.clear();
    for(int i=0; i<n; ++i){
      cin>>x>>y>>v>>b;
      if((x!=0&&x!=r)&&(y!=0&&y!=c)){
        continue;
      }
      if((v!=0&&v!=r)&&(b!=0&&b!=c)){
        continue;
      }
      if(y==0)
        tmp=r+r-x;
      else
        tmp=x;
      if(x==r)
        tmp+=c+c-y;
      else
        tmp+=y;
      if(x==0&&y==0)
        tmp=0;
      a.push_back(mk(tmp, i));
      x=v;
      y=b;
      if(y==0)
        tmp=r+r-x;
      else
        tmp=x;
      if(x==r)
        tmp+=c+c-y;
      else
        tmp+=y;
      if(x==0&&y==0)
        tmp=0;
      a.push_back(mk(tmp, i));
    }
    sort(a.begin(), a.end());
    n=a.size();
    bool l=1;
    stack <int> b;
    int tp;
    for(int i=0; i<n; ++i){
      if(b.size()==0){
        b.push(a[i].sc);
        continue;
      }
      tp=b.top();
      if(tp==a[i].sc)
        b.pop();
      else
        b.push(a[i].sc);
    }
    if(b.size()==0)
      cout<<"YES"<<endl;
    else
      cout<<"NO"<<endl;
  }
  return 0;
}