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;
#define ll long long
#define db double
#define pii pair<int,int>
#define pli pair<ll,int>
#define pil pair<int,ll>
#define pll pair<ll,ll>
#define mat vector<vector<int>>
const int inf = 1 << 30;
const ll linf = 1e18;
const db EPS = 1e-7;
template<class T> void chmin(T& x, T y){if(x > y) x = y;}
template<class T> void chmax(T& x, T y){if(x < y) x = y;}

int R, C, N;

bool judge(int x, int y){
    return (x == 0 || x == R || y == 0 || y == C);
}

int culc_dist(int x, int y){
    if(x == 0) return y;
    if(y == C) return x + C;
    if(x == R) return R + C + (C - y);
    if(y == 0) return R * 2 + C * 2 - x;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cin >> R >> C >> N;
    vector<pii> dat;
    for(int i = 0; i < N; i++){
        int x1, y1, x2, y2;
        cin >> x1 >> y1 >> x2 >> y2;
        if(judge(x1, y1) && judge(x2, y2)){
            dat.emplace_back(pii{culc_dist(x1, y1), i});
            dat.emplace_back(pii{culc_dist(x2, y2), i});
        }
    }
    sort(dat.begin(), dat.end());
    stack<int> st;
    st.push(dat[0].second);
    for(int i = 1; i < dat.size(); i++){
        if(st.empty() || st.top() != dat[i].second) st.push(dat[i].second);
        else st.pop();
    }
    cout << (st.empty() ? "YES" : "NO") << endl;
    return 0;
}