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 <algorithm>
#include <iostream>
using namespace std;
typedef pair<int, int> P;

int main()
{
    int r, c, n;
    cin >> r >> c >> n;
    int k = 0;
    P p[100002];
    for(int i = 0; i < n; i++){
        int x[2], y[2];
        cin >> x[0] >> y[0] >> x[1] >> y[1];
        int t[2] = {-1, -1};
        for(int j = 0; j < 2; j++){
            if(y[j] == 0 || x[j] == r) t[j] = x[j] + y[j];
            else if(y[j] == c || x[j] == 0) t[j] = r * 2 + c * 2 - (x[j] + y[j]);
        }
        sort(t, t + 2);
        if(t[0] == -1) continue;
        p[k] = P(t[0], t[1]);
        k++;
    }
    sort(p, p + k);
    int d = 0;
    while(d < k){
        for(int i = d + 1; i <= k; i++){
            if(i == k || p[i].first > p[d].second){
                d = i;
                break;
            }
            if(p[i].second > p[i - 1].second){
                cout << "NO" << endl;
                return 0;
            }
        }
    }
    cout << "YES" << endl;
}