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 <iostream>
#include <utility>
#include <vector>
#include <algorithm>
#include <stack>
using namespace std;

using int64 = long long;

int64 R, C;
int N;

int64 calc(int64 x, int64 y) {
    if (y == 0) return x; 
    else if (x == R) return R + y;
    else if (y == C) return R + C + (R - x);
    else return R + C + R + (C - y);
}

int main() {
    cin >> R >> C >> N;

    vector<pair<int64, int>> vec;
    for (int i = 0; i < N; i++) {
        int64 x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        if ((x1 != 0) and (x1 != R) and (y1 != 0) and (y1 != C)) continue;
        if ((x2 != 0) and (x2 != R) and (y2 != 0) and (y2 != C)) continue;
        vec.emplace_back(calc(x1, y1), i);
        vec.emplace_back(calc(x2, y2), i);
    }

    sort(vec.begin(), vec.end());

    stack<int> st;
    static bool used[200000] = {};
    for (auto& p : vec) {
        if (!used[p.second]) {
            used[p.second] = true;
            st.push(p.second);
        } else if (st.top() != p.second) {
            cout << "NO" << endl;
            return 0;
        } else {
            st.pop();
        }
    }
    cout << "YES" << endl;

    return 0;
}