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)

// Crt. 2019-12-15  17:22:21, 20:12:00
#include <algorithm>
#include <iostream>
#include <cstdio>
#define N 100005
using namespace std;
const int eps = 1e8 + 7;

int r, c, s, n, m, a[N], b[N], top, stk[N], sh[N], in[N], out[N];

inline bool inr(int x, int y) {
    return x && x < r && y && y < c;
}

inline int getid(int x, int y) {
    if (!x && y > 0) return y;
    if (y == c && x > 0) return x + eps;
    if (x == r && y < c) return c - y + eps * 2;
    if (!y && x < r) return r - x + eps * 3;
    puts("-1"), exit(0);
}

int main() {
#ifdef LOCAL_JUDGE
    freopen("work.in", "r", stdin);
    freopen("work.out", "w", stdout);
#endif

    cin >> r >> c >> n;

    for (int i = 1, x, y, xx, yy; i <= n; ++i) {
        scanf("%d%d%d%d", &x, &y, &xx, &yy);
        if (inr(x, y) || inr(xx, yy)) continue;
        //cout << x << " " << y << " " << xx << " " << yy << endl;
        a[++m] = getid(x, y), b[m] = getid(xx, yy);
        if (a[m] > b[m]) swap(a[m], b[m]);
        sh[++s] = a[m], sh[++s] = b[m];
    }

    sort(sh + 1, sh + s + 1);

    for (int i = 1; i <= m; ++i) {
        //cout << a[i] << " " << b[i] << endl;
        in[a[i] = lower_bound(sh + 1, sh + s + 1, a[i]) - sh] = i,
        out[b[i] = lower_bound(sh + 1, sh + s + 1, b[i]) - sh] = i;
    }

    for (int i = 1; i <= s; ++i) {
        if (in[i]) stk[++top] = in[i];
        if (out[i]) {
            if (stk[top] != out[i]) return puts("NO"), 0;
            --top;
        }
    }

    puts("YES");

    return 0;
}