Broken car race

#include <bits/stdc++.h>
#define int long long
using namespace std;

const int mod = 1e9+7;
using P = pair<int, int>;

void printA(P p) { cout << "(" << p.first << " " << p.second << ")\n";}
int inLine(int ax, int ay, int bx, int by, int cx, int cy)
{
    int Ax = bx-ax;
    int Ay = by-ay;
    int Bx = cx-bx;
    int By = cy-by;

    return Ax*By - Bx*Ay;
}

vector<P> order(P p1, P p2, P p3, P p4)
{
    vector<P> Ps = {p1, p2, p3, p4};
    for (int i = 1; i < 4; i++)
    {
        for (int j = 1; j < 4; j++)
        {
            if (j == i)
                continue;
            set<P> used{p2, p3, p4};
            used.erase(Ps[i]);
            used.erase(Ps[j]);
            P last;
            for (P elem : used)
                last = elem;
            // we have Ps[0], Ps[i] Ps[j], last

            int sign1 = inLine(Ps[0].first, Ps[0].second, Ps[i].first, Ps[i].second, Ps[j].first, Ps[j].second);
            int sign2 = inLine(Ps[i].first, Ps[i].second, Ps[j].first, Ps[j].second, last.first, last.second);
            int sign3 = inLine(Ps[j].first, Ps[j].second, last.first, last.second, Ps[0].first, Ps[0].second);
            int sign4 = inLine(last.first, last.second, Ps[0].first, Ps[0].second, Ps[i].first, Ps[i].second);

            if ((sign1 <= 0 && sign2 <= 0 && sign3 <= 0 && sign4 <= 0) || (sign1 >= 0 && sign2 >= 0 && sign3 >= 0 && sign4 >= 0))
            {
                // Found
                if (sign1 > 0)
                {
                    return {Ps[0], Ps[i], Ps[j], last};
                }
                else
                    return {last, Ps[j], Ps[i], Ps[0]};
                
            }
        }
    }
    return {};
}

signed main() {
    int n;
    cin >> n;

    vector<pair<int, int>> dots(n);

    for (int i = 0; i < n; i++)
    {
        int x, y;
        cin >> x >> y;
        dots[i] = {x, y};
    }

    if (n < 4)
    {
        cout << "NO";
        return 0;
    }

    if (n == 4)
    {
        vector<P> res = order(dots[0], dots[1], dots[2], dots[3]);
        if (res.size() > 0)
        {
            cout << "YES\n";
            cout << res[0].first << " " << res[0].second << "\n";
            cout << res[1].first << " " << res[1].second << "\n";
            cout << res[2].first << " " << res[2].second << "\n";
            cout << res[3].first << " " << res[3].second << "\n";
        }
        else
        {
            cout << "NO";
        }
        return 0;
    }

    if (n > 4)
    {
        set<P> points = {dots[0], dots[1], dots[2], dots[3], dots[4]};
        for (int i = 0; i < 5; i++)
        {
            set<P> p2 = points;
            p2.erase(dots[i]);

            vector<P> pointArr;
            for (P p : p2)
                pointArr.push_back(p);

            vector<P> res = order(pointArr[0], pointArr[1], pointArr[2], pointArr[3]);
            if (res.size() > 0)
            {
                cout << "YES\n";
                cout << res[0].first << " " << res[0].second << "\n";
                cout << res[1].first << " " << res[1].second << "\n";
                cout << res[2].first << " " << res[2].second << "\n";
                cout << res[3].first << " " << res[3].second << "\n";
                return 0;
            }
        }
    }
    cout << "NO";
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED