Broken car race

#include <bits/stdc++.h>
typedef long long ll;
typedef long double ld;
using namespace std;
#define F first
#define S second
#define X real()
#define Y imag()

typedef complex<ll> co;

bool ccw(co a, co b, co c) {
    return ((c-a)*conj(b-a)).Y>0;
}

co points[101010];

vector<co> convexHull(int n) {
    auto cmp = [](co a, co b) {
        if (a.X==b.X) return a.Y<b.Y;
        else return a.X<b.X;
    };
    sort(points,points+n,cmp);
    vector<co> hull;
    if (n<=2) {
        for (int i=0;i<n;i++) hull.push_back(points[i]);
        return hull;
    }
    hull.push_back(points[0]);
    for (int d=0;d<2;d++) {
        if (d) reverse(points,points+n);
        size_t s = hull.size();
        for (int i=1;i<n;i++) {
            while (hull.size()>s&&!ccw(hull[hull.size()-2],hull.back(),points[i])) {
                hull.pop_back();
            }
            hull.push_back(points[i]);
        }
    }
    hull.pop_back();
    return hull;
}

int main() {
    int n;
    cin>>n;
    for (int i=0;i<n;i++) {
        ll x,y;
        cin>>x>>y;
        points[i] ={x,y};
    }
    if (n<4) {
        cout<<"NO\n";
        return 0;
    }
    vector<co> hull = convexHull(n);
    if (hull.size()>3) {
        cout<<"YES\n";
        for (int i=0;i<4;i++) cout<<hull[i].X<<" "<<hull[i].Y<<"\n";
        return 0;
    }
    if (n==4) {
        cout<<"NO\n";
        return 0;
    }
    vector<co> inner;
    for (int i=0;i<n && inner.size()<2;i++) {
        bool ok=true;
        for (co h : hull) {
            if (h==points[i]) ok=false;
        }
        if (ok) inner.push_back(points[i]);
    }
    bool side[3];
    int cnt=0;
    for (int i=0;i<3;i++) {
        side[i] = ccw(inner[0],inner[1],hull[i]);
        if (side[i]) cnt++;
    }
    cnt--;
    if (cnt) {
        int ind=0;
        for (int i=0;i<3;i++) {
            if (side[i]) {
                points[ind]=hull[i];
                ind++;
            }
        }
    } else {
        int ind=0;
        for (int i=0;i<3;i++) {
            if (!side[i]) {
                points[ind]=hull[i];
                ind++;
            }
        }
    }
    points[2] = inner[0];
    points[3] = inner[1];
    vector<co> ans = convexHull(4);
    cout<<"YES\n";
    for (co z : ans) cout<<z.X<<" "<<z.Y<<"\n";
}

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