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++11 (GCC 4.8.1) (judge verdict: Accepted)

#include <iostream>
#include <algorithm>
#include <iomanip>
#include <string>
#include <functional>
#include <utility>
#include <queue>
#include <vector>
#include <string>
#include <stack>
#define rep(i,n) for(ll i=0;i<n;i++)
using namespace std;
typedef long long int ll;
const ll  MOD = 1000000007;
typedef pair<ll,ll> P;
const ll INF = 100100100100100100;

ll H,W,N;
ll x,y;
vector<P> a,b,c,d;
vector<ll> q;
vector<ll> mem;
ll cnt[100100];
bool aaa[100100];
int main(){
  cin >> H >> W >> N;
  rep(i,N*2){
    cin >> y >> x;
    if(y == 0){
      a.push_back(make_pair(x,i/2));
    }
    else if(x == W){
      b.push_back(make_pair(y,i/2));
    }
    else if(y == H){
      c.push_back(make_pair(-x,i/2));
    }
    else if(x == 0){
      d.push_back(make_pair(-y,i/2));
    }
  }
  sort(a.begin(),a.end());
  sort(b.begin(),b.end());
  sort(c.begin(),c.end());
  sort(d.begin(),d.end());
  rep(i,a.size()){
    cerr << a[i].second << " ";
    q.push_back(a[i].second);
  }
  cerr << endl;
  rep(i,b.size()){
    cerr << b[i].second << " ";
    q.push_back(b[i].second);
  }
  cerr << endl;
  rep(i,c.size()){
    cerr << c[i].second << " ";
    q.push_back(c[i].second);
  }
  cerr << endl;
  rep(i,d.size()){
    cerr << d[i].second << " ";
    q.push_back(d[i].second);
  }
  cerr << endl;
  rep(i,q.size()){
    cerr << q[i] << " ";
    cnt[q[i]]++;
  }
  cerr << endl;
  ll now_p = -1;
  rep(i,q.size()){
    ll tmp = q[i];
    if(cnt[tmp] == 1) continue;
    cerr << tmp << " ";
    if(now_p == -1){
      mem.push_back(tmp);
      now_p = 0;
      aaa[tmp] = true;
    }
    else{
      if(mem[now_p] == tmp){
        now_p--;
        mem.pop_back();
        aaa[tmp] = false;
      }
      else if(aaa[tmp]){
        cout << "NO" << endl;
        return 0;
      }
      else{
        now_p++;
        mem.push_back(tmp);
        aaa[tmp] = true;
      }
    }
  }
  cout << "YES" << endl;
}