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>
using namespace std;

#define maxn 211111
typedef pair<int, int> pii;
pii a[maxn][2], b[maxn];
int val[maxn], sval[maxn];
int d[maxn][2];
int m;
int n, r, c;

void addpoint(pii x)
{
    b[++m] = x;
}

bool onborder(pii x)
{
    return x.first == 0 || x.first == c || x.second == 0 || x.second == r;
}

int getid(pii x)
{
    if (x.first == 0)
    {
        return 1;
    }
    if (x.second == r)
    {
        return 2;
    }
    if (x.first == c)
    {
        return 3;
    }
    if (x.second == 0)
    {
        return 4;
    }
}

int cmp(pii x, pii y)
{
    int lid1 = getid(x);
    int lid2 = getid(y);
    if (lid1 != lid2)
    {
        return lid1 < lid2;
    }
    if (lid1 == 1)
    {
        return x.second < y.second;
    }
    if (lid1 == 2)
    {
        return x.first < y.first;
    }
    if (lid1 == 3)
    {
        return x.second > y.second;
    }
    if (lid1 == 4)
    {
        return x.first > y.first;
    }
}

int main()
{
    cin >> r >> c >> n;
    for (int i = 1; i <= n; i++)
    {
        cin >> a[i][0].first >> a[i][0].second;
        cin >> a[i][1].first >> a[i][1].second;

        if (onborder(a[i][0]))
        {
            addpoint(a[i][0]);
        }
        if (onborder(a[i][1]))
        {
            addpoint(a[i][1]);
        }

    }

    set<pii> st;
    for (int i = 1; i <= m; i++)
    {
        st.insert(b[i]);
    }
    m = 0;
    for (auto x : st)
    {
        b[++m] = x;
    }

    sort(b + 1, b + 1 + m, cmp);

    map<pii, int> pos;
    for (int i = 1; i <= m; i++)
    {
        pos[b[i]] = i;
    }

    for (int i = 1; i <= n; i++)
    {
        if (!onborder(a[i][0]))
        {
            continue;
        }
        if (!onborder(a[i][1]))
        {
            continue;
        }
        d[i][0] = pos[a[i][0]];
        d[i][1] = pos[a[i][1]];
        if (d[i][0] > d[i][1])
        {
            swap(d[i][0], d[i][1]);
        }
        if (d[i][0] + 1 == d[i][1])
        {
            continue;
        }
    }

    for (int i = 1; i <= n; i++)
    {
        if (d[i][0] + 1 == d[i][1])
        {
            continue;
        }
        if (!d[i][0])
        {
            continue;
        }
        val[d[i][0]]++;
        val[d[i][1]]--;
    }

    for (int i = 1; i <= m; i++)
    {
        sval[i] = sval[i - 1] + val[i];
    }

    for (int i = 1; i <= n; i++)
    {
        int x = d[i][0] + 1;
        int y = d[i][1] - 1;
        if (sval[y] - sval[x - 1])
        {
            cout << "NO" << endl;
            return 0;
        }
    }

    cout << "YES" << endl;
    return 0;
}