#include <iostream>
#include <cstdio>
#include <vector>
using namespace std;

class Point{
    public:
  int x;
  int y;
  Point(int x, int y){
      this->x=x;
      this->y=y;
  }
  int get_x(){
      return x;
  }
  int get_y(){
      return y;
  }
};

int simetricx(int x1, int x2 ){
   int x3=2*x2-x1;

    return x3;
}
int simetricy(int y1, int y2){
    int y3=2*y2-y1;
    return y3;
}

int main(){

    int k;
    cin>>k;
    for(int j=0;j<k;j++){
        int n;
        cin>>n;
        vector<Point>coord;
        if(n%2!=0) cout<<'0'<<"\n";
        else{
            int sumax=0, sumay=0;
            for(int i=0;i<n;i++){
                int x,y;
                cin>>x>>y;
                Point punct(x,y);
                coord.push_back(punct);
                sumax=sumax+x;
                sumay=sumay+y;
            }
            int p=0;
            int Gx,Gy;

            if(sumax==0)Gx=0;
            else Gx=sumax/n;

            if(sumay==0)Gy=0;
            else Gy=sumay/n;

            if(Gx==Gy){
                cout<<'1'<<' ';
                float gx=Gx, gy=Gy;
                printf("%.4f %.4f\n",gx,gy);

            }
            else {
                for(int i=0;i<n-1;i++){
                int Ax,Ay;
                Ax=simetricx(coord[i].get_x(),Gx);
                Ay=simetricx(coord[i].get_y(),Gy);

                for(int b=i;b<n;b++)
                    if(Ax==coord[b].get_x()&&Ay==coord[b].get_y()){
                        p++;
                        cout<<p<<' ';
                        float gx=Gx;
                        float gy=Gy;
                        printf("%.4f %.4f\n",gx,gy);

                    }

                }
                if(p==0) cout<<'0'<<"\n";
            }

            }

            coord.clear();
        }
        return 0;

    }