# include <bits/stdc++.h>
using namespace std;
int f;
struct point
{
    double x;
    double y;
};
vector <point> fig[505];
point newpoint;
double mx,my;
stack <point> s;
double Const = 1.0;
double sums[505];
double xans[505],yans[505];
double alphaans[505];
int type[505];
vector <point> help;
vector <int> types[8];
vector <point> p[2];
double PI = 3.14159265;
double SUM,ANS;
int otg1=-1,otg2=-1;
double TL = 3.6;
clock_t begin1;
bool cmp(point i, point j)
{
    double tx,ty,px,py;
    tx=i.x-mx;
    ty=i.y-my;
    px=j.x-mx;
    py=j.y-my;
    if(tx*py-ty*px>0)return true;
    if(tx*py-ty*px==0)return i.x>j.x;
    return false;
    //if(i.cp==j.cp)return i.x<j.x;
    //return i.cp<j.cp;
}
bool cmpbyx(point i, point j)
{
    if(i.x==j.x)return i.y<j.y;
    return i.x<j.x;
}
double Area(int pos)
{
  double S = 0;
 // cout<<"THIS IS "<<pos<<"::"<<endl;
 // cout<<fig[pos][0].x<<" "<<fig[pos][0].y<<endl;
  for(int i = 1; i < fig[pos].size()-1; ++i)
  {
     // cout<<fig[pos][i].x<<" "<<fig[pos][i].y<<endl;
    double x1 = fig[pos][i].x - fig[pos][0].x;
    double y1 = fig[pos][i].y - fig[pos][0].y;
    double x2 = fig[pos][i+1].x - fig[pos][0].x;
    double y2 = fig[pos][i+1].y - fig[pos][0].y;
    S += x1*y2 - x2*y1;
  }
 // cout<<endl<<endl;
  return abs(S/2);
}
void checkrectangle(int v)
{
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
    for(i=1;i<fig[v].size();i++)
    {
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    bool fl = true;
    for(i=1;i<=4;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x)fl=0;
    }
    for(i=5;i<10;i++)
    {
        if(fig[v][i].x!=fig[v][5].x)fl=0;
    }
    if(fl==1)
    {
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=1;
        alphaans[v]=0;
        return ;
    }
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);

    for(i=1;i<=4;i++)
    {
        // cout<<fig[v][i].x<<"^^^"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x)fl=0;
    }
    for(i=5;i<10;i++)
    {
       //  cout<<fig[v][i].x<<"%%%%"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][5].x)fl=0;
    }
   // cout<<fl<<endl;
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=1;
        alphaans[v]=90;
        return ;
    }
     for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
     for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
     for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype2(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][8].x||fig[v][4].y!=fig[v][8].y)fl=0;
    if(fig[v][8].x!=fig[v][9].x||fig[v][8].y+1!=fig[v][9].y)fl=0;

    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=2;
        alphaans[v]=0;
        return ;
    }
    //////////////////////////////////////////////////////position 2
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
 for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;
     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][8].x||fig[v][4].y!=fig[v][8].y)fl=0;
    if(fig[v][8].x!=fig[v][9].x||fig[v][8].y+1!=fig[v][9].y)fl=0;

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=2;
        alphaans[v]=90;
        return ;
    }
    //////////////////////////position 3
    fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
 for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;
     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][8].x||fig[v][4].y!=fig[v][8].y)fl=0;
    if(fig[v][8].x!=fig[v][9].x||fig[v][8].y+1!=fig[v][9].y)fl=0;

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=2;
        alphaans[v]=180;
        return ;}
        /////////////////////////// position 4
        fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
 for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;
     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][8].x||fig[v][4].y!=fig[v][8].y)fl=0;
    if(fig[v][8].x!=fig[v][9].x||fig[v][8].y+1!=fig[v][9].y)fl=0;
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=2;
        alphaans[v]=270;
        return ;
    }
      for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype3(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=1;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][2].x||fig[v][0].y!=fig[v][2].y)fl=0;

     for(i=3;i<=5;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][2].x+1!=fig[v][6].x||fig[v][2].y!=fig[v][6].y)fl=0;
   for(i=7;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=3;
        alphaans[v]=0;
        return ;
    }
    //////////////////////////////////////////////////////position 2
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
  for(i=1;i<=1;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][2].x||fig[v][0].y!=fig[v][2].y)fl=0;

     for(i=3;i<=5;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][2].x+1!=fig[v][6].x||fig[v][2].y!=fig[v][6].y)fl=0;
   for(i=7;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=3;
        alphaans[v]=90;
        return ;
    }
    //////////////////////////position 3
    fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
   for(i=1;i<=1;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][2].x||fig[v][0].y!=fig[v][2].y)fl=0;

     for(i=3;i<=5;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][2].x+1!=fig[v][6].x||fig[v][2].y!=fig[v][6].y)fl=0;
   for(i=7;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=3;
        alphaans[v]=180;
        return ;}
        /////////////////////////// position 4
        fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
  for(i=1;i<=1;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][2].x||fig[v][0].y!=fig[v][2].y)fl=0;

     for(i=3;i<=5;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][2].x+1!=fig[v][6].x||fig[v][2].y!=fig[v][6].y)fl=0;
   for(i=7;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=3;
        alphaans[v]=270;
        return ;
    }
      for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype4(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][5].x+1!=fig[v][8].x||fig[v][5].y!=fig[v][8].y)fl=0;
   for(i=9;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=4;
        alphaans[v]=0;
        return ;
    }
    //////////////////////////////////////////////////////position 2
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][5].x+1!=fig[v][8].x||fig[v][5].y!=fig[v][8].y)fl=0;
   for(i=9;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=4;
        alphaans[v]=90;
        return ;
    }
    //////////////////////////position 3
    fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
     for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][5].x+1!=fig[v][8].x||fig[v][5].y!=fig[v][8].y)fl=0;
   for(i=9;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=4;
        alphaans[v]=180;
        return ;}
        /////////////////////////// position 4
        fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
     for(i=1;i<=3;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=5;i<=7;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][5].x+1!=fig[v][8].x||fig[v][5].y!=fig[v][8].y)fl=0;
   for(i=9;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=4;
        alphaans[v]=270;
        return ;
    }
      for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype5(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][3].x||fig[v][0].y!=fig[v][3].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][7].x||fig[v][4].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=5;
        alphaans[v]=0;
        return ;
    }
    //////////////////////////////////////////////////////position 2
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
        for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][3].x||fig[v][0].y!=fig[v][3].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][7].x||fig[v][4].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=5;
        alphaans[v]=90;
        return ;
    }
    //////////////////////////position 3
    fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
       for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][3].x||fig[v][0].y!=fig[v][3].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][7].x||fig[v][4].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=5;
        alphaans[v]=180;
        return ;}
        /////////////////////////// position 4
        fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
       for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][3].x||fig[v][0].y!=fig[v][3].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][4].x+1!=fig[v][7].x||fig[v][4].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=5;
        alphaans[v]=270;
        return ;
    }
      for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype6(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=10)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][3].x+1!=fig[v][7].x||fig[v][3].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y+1;
        type[v]=6;
        alphaans[v]=0;
        return ;
    }
    //////////////////////////////////////////////////////position 2
    fl=1;
    double x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
     for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][3].x+1!=fig[v][7].x||fig[v][3].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y+1;
        type[v]=6;
        alphaans[v]=90;
        return ;
    }
    //////////////////////////position 3
    fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
     for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][3].x+1!=fig[v][7].x||fig[v][3].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }

    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y+1;
        type[v]=6;
        alphaans[v]=180;
        return ;}
        /////////////////////////// position 4
        fl=1;
 x,y;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
     for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][4].x||fig[v][0].y!=fig[v][4].y)fl=0;

     for(i=4;i<=6;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][3].x+1!=fig[v][7].x||fig[v][3].y!=fig[v][7].y)fl=0;
   for(i=8;i<=9;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
    x = -fig[v][0].x;
y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y+1;
        type[v]=6;
        alphaans[v]=270;
        return ;
    }
      for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
}
void checktype7(int v)
{
   // cout<<"              "<<v<<" : "<<endl;
    int i;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    help.clear();
    help.push_back(fig[v][0]);
  //  cout<<fig[v][0].x<<" "<<fig[v][0].y<<endl;
    for(i=1;i<fig[v].size();i++)
    {
      //  cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
        if((fig[v][i].x!=fig[v][i-1].x)||(fig[v][i].y!=fig[v][i-1].y))help.push_back(fig[v][i]);
    }
    fig[v].clear();
    for(i=0;i<help.size();i++)
    {
         fig[v].push_back(help[i]);
        // cout<<help[i].x<<" "<<help[i].y<<endl;
    }
//cout<<endl<<endl;
    if(fig[v].size()!=9)return ;
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    int j;
    //////////////////////////////////position 1
    bool fl = true;
    for(i=1;i<=2;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][0].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0; // cout<<fl<<endl;
    }
    if(fig[v][0].x+1!=fig[v][3].x||fig[v][0].y!=fig[v][3].y)fl=0;

     for(i=4;i<=5;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fig[v][3].x+1!=fig[v][6].x||fig[v][3].y!=fig[v][6].y)fl=0;
   for(i=7;i<=8;i++)
    {
       // cout<<fig[v][i].x<<"&&&"<<fig[v][i].y<<endl;
        if(fig[v][i].x!=fig[v][i-1].x||fig[v][i].y-1!=fig[v][i-1].y)fl=0;
    }
    if(fl==1)
    {
       // cout<<v<<" : "<<endl;
       // for(i=0;i<fig[v].size();i++)
         //   cout<<fig[v][i].x<<" "<<fig[v][i].y<<endl;
   // cout<<endl<<endl;
        double x = -fig[v][0].x;
        double y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;
        type[v]=7;
        alphaans[v]=0;
        return ;
    }

}

void input()
{
    cin>>f;
    int i,j,p;
    double u,v;
    int m,k,t;
    double sum;
    for(i=1;i<=f;i++)
    {
        cin>>p;
        for(j=1;j<=p;j++)
        {
            cin>>u>>v;
            newpoint.x=u;
            newpoint.y=v;
            fig[i].push_back(newpoint);
        }
        cin>>m;
        sum=0;
        for(j=1;j<=m;j++)
        {
            cin>>k;
            for(t=1;t<=k;t++)
                {
                    cin>>p;
                    fig[f+1].push_back(fig[i][p]);
                }
                sum+=Area(f+1);
                fig[f+1].clear();
        }
      //  for(j=0;j<fig[i].size();j++)
        //    cout<<fig[i][j].x<<" "<<fig[i][j].y<<endl;
       // cout<<endl;
        sums[i]=sum;
        checkrectangle(i);
        checktype2(i);
        checktype3(i);
        checktype4(i);
        checktype5(i);
        checktype6(i);
        checktype7(i);

       // cout<<i<<" : "<<type[i]<<" "<<alphaans[i]<<endl;
    }
}
double rotate(int v, bool fl, double arad)
{
    int i;
    p[fl].clear();
    point A;
    double cosa = (cos(arad));
    double sina = (sin(arad));
    double miny=1000000.0,minx;
    for(i=0;i<fig[v].size();i++)
    {
        A.x = (cosa*fig[v][i].x - fig[v][i].y*sina);
        A.y = (cosa*fig[v][i].y + fig[v][i].x*sina);
        if(miny>A.y){miny=A.y;minx=A.x;}
        else
        if(miny-A.y<=0.0000001&&minx>A.x){miny=A.y;minx=A.x;}
        p[fl].push_back(A);
    }
    //return {-minx,-miny};
}

double grahamscan(int pos)
{

    int i,j;
    int m=0;
    for(i=0;i<fig[pos].size();i++)
    {
        if(fig[pos][i].x<fig[pos][m].x)m=i;
        else
        if((fig[pos][i].x==fig[pos][m].x)&&(fig[pos][i].y<fig[pos][m].y))m=i;
    }
    swap(fig[pos][0],fig[pos][m]);
    mx=fig[pos][0].x;
    my=fig[pos][0].y;
    sort(fig[pos].begin()+1,fig[pos].end(),cmp);
  //  for(i=0;i<fig[pos].size();i++)
     //   cout<<fig[pos][i].x<<" & "<<fig[pos][i].y<<endl;
    double S1 = sums[pos];
    s.push(fig[pos][0]);
    s.push(fig[pos][1]);
    point A,B,C;
    double tx,ty,px,py,S;
    for(i=2;i<fig[pos].size();i++)
    {
         B=s.top();
    s.pop();
    A=s.top();
    C=fig[pos][i];
    tx=B.x-A.x;
    ty=B.y-A.y;
    px=C.x-A.x;
    py=C.y-A.y;
    S=(double)(tx*py-ty*px);
   // cout<<S<<" "<<A.x<<" "<<A.y<<"   "<<B.x<<" "<<B.y<<"   "<<C.x<<" "<<C.y<<" "<<tx<<" "<<ty<<" "<<px<<" "<<py<<endl;
    if(S>=0){s.push(B);s.push(C);}
    else
        s.push(C);
    }
    fig[pos].clear();
    while(!s.empty())
    {
        fig[pos].push_back(s.top());
        s.pop();
    }
    double S2 = Area(pos);
   // double ans = S2 - Const*S1;
    //cout<<S1<<" "<<S2<<endl;
    return S2;
}
double trywith(int v1, int v2)
{
    int i,j;
    point A,B;
    double alpharad,tgalpha;
    double betharad,tgbetha;
    pair <double,double > p0,p1;
    bool pos,pos1;
    point C,D;
    int q;
    double area,ans;
    int k;
    for(i=0;i<fig[v1].size();i++)
    {
        if((clock()-begin1)/CLOCKS_PER_SEC>TL)return 0;
        A = fig[v1][i];
        B = (fig[v1].size()==i+1 ? fig[v1][0] : fig[v1][i+1]);
        if(B.x-A.x!=0){
         tgalpha = (A.y-B.y)/(B.x-A.x);
         alpharad = atan(tgalpha);
        }else
        {
            if(A.y>B.y)
             alpharad = PI/2;
             else
                alpharad = 3*PI/2;
        }

         rotate(v1,0,alpharad);

 //  cout<<A.x<<" "<<A.y<<" : "<<B.x<<" "<<B.y<<" : "<<tgalpha<<" "<<alpharad<<" "<<alpharad*180/PI<<endl;


    pos=true;
  double x1 = p[0][i].x;
            double y1 = p[0][i].y;

        for(j=0;j<p[0].size();j++)
        {
            if(p[0][j].y-y1<-0.0000001)pos=0;
   //        cout<<p[0][j].x-x1<<" "<<p[0][j].y-y1<<endl;
        }
   //   cout<<endl<<endl;


        for(j=0;j<fig[v2].size();j++)
        {
   //     for(q=0;q<fig[v2].size();q++)
  //  cout<<fig[v2][q].x<<"&&"<<fig[v2][q].y<<endl;
// cout<<endl<<endl;
            C = fig[v2][j];
            D = (fig[v2].size()==j+1 ? fig[v2][0] : fig[v2][j+1]);
            if(D.x-C.x!=0){
            tgbetha = (C.y-D.y)/(D.x-C.x);
            betharad = atan(tgbetha);}else
            {
                if(C.y>D.y)
                 betharad=PI/2;
                 else
                    betharad=3*PI/2;
            }


            rotate(v2,1,betharad);

  //         cout<<C.x<<" "<<C.y<<" : "<<D.x<<" "<<D.y<<" : "<<tgbetha<<" "<<betharad<<" "<<betharad*180/PI<<endl;
  //          for(q=0;q<p[1].size();q++)
  //              cout<<p[1][q].x<<"$$$"<<p[1][q].y<<endl;
    //        cout<<endl;
   x1 = p[1][j].x;
            y1 = p[1][j].y;

            pos1 = true;for(q=0;q<p[1].size();q++){
            if(p[1][q].y-y1<-0.0000001)pos1=0;
   //        cout<<p[1][q].x-x1<<" "<<p[1][q].y-y1<<endl;
            }
   //       cout<<endl<<endl<<endl<<endl;
           k = j;
  //      cout<<pos<<"::"<<pos1<<endl;
            if(pos==pos1)
            {
                betharad = (betharad+PI);
                if(betharad>=2*PI)betharad-=2*PI;
                fig[f+1].clear();
                for(q=0;q<p[1].size();q++)
                    fig[f+1].push_back(p[1][q]);

                rotate(f+1,1,PI);
                swap(C,D);
                k = j+1;
                if(k==fig[v2].size())k=0;
   //             for(q=0;q<p[1].size();q++)
   //                 cout<<p[1][q].x<<"**"<<p[1][q].y<<endl;
   //             cout<<endl;
            }
    //        cout<<k<<" "<<p[1][k].x<<" "<<p[1][k].y<<endl;
                        fig[f+1].clear();
             x1 = p[0][i].x;
             y1 = p[0][i].y;
            for(q=0;q<p[0].size();q++)
            {
                p[0][q].x-=x1;
                p[0][q].y-=y1;
                fig[f+1].push_back(p[0][q]);
    //            cout<<p[0][q].x<<" "<<p[0][q].y<<endl;
                 p[0][q].x+=x1;
                p[0][q].y+=y1;

            }
            x1 = p[1][k].x;
            y1 = p[1][k].y;
            for(q=0;q<p[1].size();q++)
            {
                p[1][q].x-=x1;
                p[1][q].y-=y1;
                fig[f+1].push_back(p[1][q]);
//cout<<p[1][q].x<<" "<<p[1][q].y<<endl;
  p[1][q].x+=x1;
                p[1][q].y+=y1;
            }

            area = grahamscan(f+1);
    //      cout<<area<<endl;
   //      for(q=0;q<fig[f+1].size();q++)
    //     cout<<fig[f+1][q].x<<" "<<fig[f+1][q].y<<endl;
  //     cout<<endl<<endl<<endl<<endl;

            if(Const*(SUM-sums[v1]-sums[v2])+area<ANS){ANS = Const*(SUM-sums[v1]-sums[v2])+area;
            otg1 = v1;
            otg2 = v2;
            alphaans[otg1]= alpharad*(180.0/PI);
            alphaans[otg2] = betharad*(180.0/PI);

            xans[otg1] = -p[0][i].x;
            yans[otg1] = -p[0][i].y;

            xans[otg2] = -p[1][k].x;
            yans[otg2] = -p[1][k].y;
            if(pos==0)
                yans[otg1]-=0.00001;
                else
                    yans[otg2]-=0.00001;
            }
   //           cout<<xans[otg1]<<" "<<yans[otg1]<<" "<<alphaans[otg1]<<endl;
  //      cout<<xans[otg2]<<" "<<yans[otg2]<<" "<<alphaans[otg2]<<endl;
   //     cout<<"NEWWW"<<endl<<endl<<endl;
        }
    }
}
void reverse(int v)
{
    double x,y;
    int i,j;
    for(i=0;i<fig[v].size();i++)
    {
        x = fig[v][i].x;
        y = fig[v][i].y;
        fig[v][i].x = -y;
        fig[v][i].y = x;
    }
    sort(fig[v].begin(),fig[v].end(),cmpbyx);
    x = -fig[v][0].x;
 y = -fig[v][0].y;
        xans[v]=x;
        yans[v]=y;

        alphaans[v]=(alphaans[v]+90);
        if(alphaans[v]>360.0)alphaans[v]-=360.0;
        return ;
}
void print()
{
   /* int i;
    double ans = 0,k;
    int p = -1;
    for(i=1;i<=f;i++)
    {
        k  = grahamscan(i);
        if(k<ans){ans=k;p=i;}
    }
    for(i=1;i<=f;i++)
    {
        if(p==i)cout<<"1 0 0 0"<<endl;
        else
        cout<<0<<endl;
    }*/

    int i;
    int br2=0;
    for(i=1;i<=f;i++)
    {
        //cout<<type[i]<<endl;
        if(type[i]>0)br2++;
        types[type[i]].push_back(i);
    }
    if(br2==f){
    int pos=0;
    for(i=0;i<types[1].size();i++)
    {
        xans[types[1][i]]+=pos;
        pos++;
    }
    int t2=0,t3=0;
    int t4=0,t6=0;
    int t5=0;
    int t7=0;
    while(types[7].size()-t7>1)
    {
        xans[types[7][t7]]+=pos;
        xans[types[7][t7+1]]+=pos;
        yans[types[7][t7+1]]+=2;
        t7+=2;
        pos+=2;
    }
  while(types[4].size()-t4>1)
    {
        if(((types[2].size()-t2)>0)&&(((types[2].size()-t2)%2==1)||((types[2].size()-t2)*2>types[6].size())))
        {
            xans[types[4][t4]]+=pos;
            yans[types[4][t4]]++;
            reverse(types[4][t4+1]);
            xans[types[4][t4+1]]+=pos;
            reverse(types[2][t2]);
            reverse(types[2][t2]);
            xans[types[2][t2]]+=(pos+1);
            yans[types[2][t2]]+=3;
            t2++;
            pos+=3;
            t4+=2;
        }
        else
            if((types[3].size()-t3)>0)
            {
                reverse(types[4][t4]);
                reverse(types[4][t4]);
                xans[types[4][t4]]+=(pos+1);
                yans[types[4][t4]]+=2;
                reverse(types[4][t4+1]);
                xans[types[4][t4+1]]+=pos;
                reverse(types[3][t3]);
                reverse(types[3][t3]);
                xans[types[3][t3]]+=pos;
                yans[types[3][t3]]++;
                pos+=3;
                t3++;
                t4+=2;
            }
            else
                break;
    }

    for(t6=0;t6<types[6].size()&&(types[2].size()-t2>1);t6++)
    {
        reverse(types[2][t2]);
        xans[types[2][t2]]+=pos;
        reverse(types[6][t6]);
        xans[types[6][t6]]+=pos;
        yans[types[6][t6]]+=1;
        reverse(types[2][t2+1]);
         reverse(types[2][t2+1]);
          reverse(types[2][t2+1]);
        xans[types[2][t2+1]]+=pos;
        yans[types[2][t2+1]]+=2;
        pos+=3;
        t2+=2;
    }

    for(t5=0;t5<types[5].size()&&(types[3].size()-t3>1);t5++)
    {
        reverse(types[3][t3]);
         reverse(types[3][t3]);
          reverse(types[3][t3]);
          xans[types[3][t3]]+=pos;
          reverse(types[5][t5]);
          xans[types[5][t5]]+=pos;
          yans[types[5][t5]]+=2;
          reverse(types[3][t3+1]);
          xans[types[3][t3+1]]+=pos;
          yans[types[3][t3+1]]+=3;
          pos+=3;
          t3+=2;
    }
    while(types[2].size()-t2>1)
    {
        xans[types[2][t2]]+=pos;
        reverse(types[2][t2+1]);
        reverse(types[2][t2+1]);
        xans[types[2][t2]]+=pos;
        yans[types[2][t2]]+=3;
        t2+=2;
        pos+=2;
    }
    while(types[3].size()-t3>1)
    {
        xans[types[3][t3]]+=pos;
        reverse(types[3][t3+1]);
        reverse(types[3][t3+1]);
        xans[types[3][t3+1]]+=pos;
        yans[types[3][t3+1]]+=1;
        pos+=2;
        t3+=2;
    }

    while(types[2].size()-t2>0&&types[3].size()-t3>0&&types[7].size()-t7>0)
    {
        xans[types[2][t2]]+=pos;
        xans[types[7][t7]]+=(pos+1);
        yans[types[7][t7]]++;
        xans[types[3][t3]]+=(pos+2);
        pos+=4;
        t7++;
        t2++;
        t3++;
    }
    while(types[2].size()-t2>0&&types[3].size()-t3>0)
    {
        yans[types[2][t2]]++;
        xans[types[2][t2]]+=pos;
        xans[types[3][t3]]+=(pos+1);
        pos+=3;
    }
    while(t5<types[5].size())
    {
        xans[types[5][t5]]+=pos;
        t5++;
        pos+=2;
    }
    while(t3<types[3].size())
    {
        xans[types[3][t3]]+=pos;
        pos+=2;
        t3++;
    }
    while(t2<types[2].size())
    {
        xans[types[2][t2]]+=pos;
        t2++;
        pos+=2;
    }
    while(t6<types[6].size())
    {
        xans[types[6][t6]]+=pos;
        t6++;
        pos+=2;
    }
    while(t7<types[7].size())
    {
        xans[types[7][t7]]+=pos;
        pos+=2;
        t7++;
    }
    while(t4<types[4].size())
    {
        xans[types[4][t4]]+=pos;
        pos+=2;
        t4++;
    }
    for(i=1;i<=f;i++)
    {

         if(type[i]>0)
            {cout<<1<<" "<<alphaans[i]<<" "<<xans[i]+br2<<" "<<yans[i]<<endl;
           // br2+=2;
            }
         else
            cout<<0<<endl;
    }
    }
else
{
    int j;
    SUM = 0;
    for(i=1;i<=f;i++)
       {
          grahamscan(i);
          SUM += sums[i];
       }
       ANS = Const*1.5*1.5*SUM;
    for(i=1;i<=f;i++)
        for(j=i+1;j<=f;j++)
    {
        trywith(i,j);
    }
    for(i=1;i<=f;i++)
    {
        if(i==otg1||i==otg2)
        {
            if(alphaans[i]<0)alphaans[i]+=360.0;
            printf("1 %.6f %.6f %.6f\n",alphaans[i],xans[i],yans[i]);
          //  cout<<1<<" "<<alphaans[i]<<" "<<xans[i]<<" "<<yans[i]<<endl;
        }
        else
            cout<<0<<endl;
    }
}

}

int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
 begin1 = clock();
freopen ("packing.in","r",stdin);
freopen("packing.out","w",stdout);
input();
int i;
for(i=1;i<f-1;i++)Const*=1.5;
//cout<<"1 0 0 0"<<endl<<"0"<<endl;
print();
}