#include <iostream>
#include <math.h>
#include <fstream>
#include <bits/stdc++.h>
using namespace std;

typedef struct
{
    double x,y;
}punct;
const int inf=1e9;
 vector<punct> v,I,J;
 double dist(punct a,punct b)
 {
     return (sqrt((b.x-a.x)*(b.x-a.x)+(b.y-a.y)*(b.y-a.y)));
 }
 double arie(punct a,punct b,punct c)
{
    double p,arie,len_a,len_b,len_c;
    len_a=dist(a,b);
    len_b=dist(b,c);
    len_c=dist(a,c);
    p=(len_a+len_b+len_c)/2;
    arie=sqrt(p*(p-len_a)*(p-len_b)*(p-len_c));
    return arie;
}
bool coliniare(punct a,punct b,punct c)
{
    int ok=0;
    double a1,a2;
    if(a.x==b.x && b.x==c.x)
    {
        return true;
    }
    if(a.y==b.y && b.y==c.y)
    {
        return true;
    }
    if(((a.x-b.x)*(b.y-c.y)-(b.x-c.x)*(a.y-b.y))==0)
    {
        return true;
    }
    return false;
}
void afisare(vector<punct> q)
{
    int i;
    for(i=0;i<q.size();i++)
    {
        cout<<q[i].x<<" "<<q[i].y<<" ";
    }
}
bool linie()
{
    punct extrem_1,extrem_2;
    double y_min=inf,y_max=-inf,x_min=inf,x_max=-inf;
    punct intern_1,intern_2;
    int i,int_1,int_2,ext_1,ext_2;
    vector<pair<int,int> > new_v;
    if(coliniare(v[0],v[1],v[2])==true && coliniare(v[1],v[2],v[3])==true)
    {
        for(i=0;i<=3;i++)
        {
            new_v.push_back({v[i].x,v[i].y});
        }
        sort(new_v.begin(),new_v.end());
        for(i=0;i<=3;i++)
        {
            v[i].x=new_v[i].first;
            v[i].y=new_v[i].second;
        }
       // afisare(v);
        extrem_1.x=v[0].x;
        extrem_1.y=v[0].y;
        extrem_2.x=v[3].x;
        extrem_2.y=v[3].y;
        intern_1.x=v[1].x;
        intern_1.y=v[1].y;
        intern_2.x=v[2].x;
        intern_2.y=v[2].y;
        I.push_back(extrem_1);
        I.push_back(extrem_2);
        J.push_back(intern_1);
        J.push_back(intern_2);
        return true;
    }
    else
    {
        return false;
    }
}
int comparator(double dif1,double dif2)
{
    if(abs(dif1-dif2)<0.001)
        return 1;
    else
        return 0;
}
bool triunghi()
{
    int i,max=0;
    punct last_p,a,b,c;
    if(arie(v[0],v[1],v[2])>max)
    {
        max=arie(v[0],v[1],v[2]);
        last_p=v[3];
        a=v[0];
        b=v[1];
        c=v[2];
    }
    if(arie(v[1],v[2],v[3])>max)
    {
        max=arie(v[1],v[2],v[3]);
        last_p=v[0];
        a=v[1];
        b=v[2];
        c=v[3];
    }
    if(arie(v[0],v[2],v[3])>max)
    {
        max=arie(v[0],v[2],v[3]);
        last_p=v[1];
        a=v[0];
        b=v[2];
        c=v[3];
    }
    if(arie(v[0],v[1],v[3])>max)
    {
        max=arie(v[0],v[1],v[3]);
        last_p=v[2];
        a=v[0];
        b=v[1];
        c=v[3];
    }
    if(comparator(arie(a,b,c),arie(a,b,last_p)+arie(a,c,last_p)+arie(b,c,last_p))==1)
    {
        I.push_back(a);
        I.push_back(b);
        I.push_back(c);
        J.push_back(last_p);
        return true;
    }
    else
    {
        return false;
    }
}
double side(punct a,punct b,punct c)
{
    return ((b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x));
}
void patrulater()
{
    punct a,b;
    a.x=v[0].x;
    a.y=v[0].y;
    b.x=v[1].x;
    b.y=v[1].y;
    if((side(a,b,v[2])<0 && side(a,b,v[3])>0) || (side(a,b,v[2])>0 && side(a,b,v[3])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[2]);
        J.push_back(v[3]);
        return;
    }
    a.x=v[0].x;
    a.y=v[0].y;
    b.x=v[2].x;
    b.y=v[2].y;
    if((side(a,b,v[1])<0 && side(a,b,v[3])>0) || (side(a,b,v[1])>0 && side(a,b,v[3])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[1]);
        J.push_back(v[3]);
        return;
    }
    a.x=v[0].x;
    a.y=v[0].y;
    b.x=v[3].x;
    b.y=v[3].y;
    if((side(a,b,v[2])<0 && side(a,b,v[1])>0) || (side(a,b,v[2])>0 && side(a,b,v[1])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[1]);
        J.push_back(v[2]);
        return;
    }
    a.x=v[1].x;
    a.y=v[1].y;
    b.x=v[2].x;
    b.y=v[2].y;
    if((side(a,b,v[0])<0 && side(a,b,v[3])>0) || (side(a,b,v[0])>0 && side(a,b,v[3])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[0]);
        J.push_back(v[3]);
        return;
    }
    a.x=v[1].x;
    a.y=v[1].y;
    b.x=v[3].x;
    b.y=v[3].y;
    if((side(a,b,v[0])<0 && side(a,b,v[2])>0) || (side(a,b,v[0])>0 && side(a,b,v[2])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[0]);
        J.push_back(v[2]);
        return;
    }
    a.x=v[2].x;
    a.y=v[2].y;
    b.x=v[3].x;
    b.y=v[3].y;
    if((side(a,b,v[0])<0 && side(a,b,v[1])>0) || (side(a,b,v[0])>0 && side(a,b,v[1])<0))
    {
        I.push_back(a);
        I.push_back(b);
        J.push_back(v[0]);
        J.push_back(v[1]);
        return;
    }
}


int main()
{
    ifstream fin("in.txt");
    punct t;
    for(int i=1;i<=4;i++)
        {fin>>t.x>>t.y;
        v.push_back(t);}

    if(linie()==true)
    {
        cout<<"Punctele sunt coliniare pe o linie\n";
        cout<<"I = ";
        afisare(I);
        cout<<"\n";
        cout<<"J = ";
        afisare(J);
        cout<<"\n";
    }
    else if(triunghi()==true)
    {
            cout<<"Punctele sunt intr-un triunghi\n";
            cout<<"I = ";
            afisare(I);
            cout<<"\n";
            cout<<"J = ";
            afisare(J);
            cout<<"\n";

    }
    else
    {
            patrulater();
            cout<<"Punctele sunt intr-un patrulater\n";
            cout<<"I = ";
            afisare(I);
            cout<<"\n";
            cout<<"J = ";
            afisare(J);
            cout<<"\n";
    }
    fin.close();
    return 0;
}