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 pb          emplace_back
#define ll          long long
#define fi          first
#define se          second
#define mp          make_pair

using namespace std;

typedef pair<int, int> pii;
const int N = int(2e5) + 7;

vector<pii> v;
int xa, ya, xb, yb, r, c, n, x1, x2;
vector<int> s;

int32_t main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
    #define Task        "test"
    if(fopen(Task".inp", "r")) {
        freopen(Task".inp", "r", stdin);
        freopen(Task".out", "w", stdout);
    }
    cin >> r >> c >> n; ++r, ++c;
    for(int i = 0; i < n; ++i) {
        cin >> xa >> ya >> xb >> yb;
        if(xa == 0) x1 = ya;
        else if(ya == c - 1) x1 = c + xa;
        else if(xa == r - 1) x1 = c + r + r - ya - 1;
        else if(ya == 0) x1 = 2 * c + r + c - xa - 1;
        else continue;
        if(xb == 0) x2 = yb;
        else if(yb == c - 1) x2 = c + xb;
        else if(xb == r - 1) x2 = c + r + r - yb - 1;
        else if(yb == 0) x2 = 2 * c + r + r - xb - 1;
        else continue;
        //cout << x1 << ' ' << x2 << '\n';
        v.pb(mp(x1, i)); v.pb(mp(x2, i));
    }
    sort(v.begin(), v.end());
    for(pii p: v) {
        if(s.size() && p.se == s.back()) s.pop_back();
        else s.pb(p.se);
    }
    cout << (s.empty() ? "YES": "NO");
}