#include <bits/stdc++.h>
#define sz(x) ((int)x.size())
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define fi first
#define se second
using namespace std;

typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;

const ll INF=4e18;

struct point {
	using T=ll;
	T x,y;
	point(){}
	point(T x,T y):x(x),y(y){}
	bool operator==(point b)const{return x==b.x&&y==b.y;}
	point operator+(point b)const{return point(x+b.x,y+b.y);}
	point operator-(point b)const{return point(x-b.x,y-b.y);}
	T operator*(point b)const{return x*b.x+y*b.y;}
	T operator/(point b)const{return x*b.y-y*b.x;}
	bool operator<(point b)const{return y==b.y?x<b.x:y<b.y;}
	inline int sgn(){return y<0||(y==0&&x<0);}
};

int n;
point v[300010];

pll a[600010];
int pr[600010];

vector<pair<pll,ll>> ans;

void manacher() {
	int len=2*n+1;
	int p=-1,r=-1;
	for(int i=0;i<len;i++) {
		if(i<=r)pr[i]=min(pr[2*p-i],r-i);
		else pr[i]=0;
		while(i-pr[i]-1>=0&&i+pr[i]+1<len&&a[i-pr[i]-1]==a[i+pr[i]+1])pr[i]++;
		if(r<i+pr[i])r=i+pr[i],p=i;
	}
}

bool is_palindrome(int l,int r) {
	int m=(l+r)/2;
	m=m*2+1;
	if((r-l)%2)m++;
	return m-pr[m]<=2*l+1;
}

void add_perpen_line(int i,int j) {
	point d=v[i]-v[j];
	ll a=2*d.x;
	ll b=2*d.y;
	ll c=-(v[i].x*v[i].x-v[j].x*v[j].x)-(v[i].y*v[i].y-v[j].y*v[j].y);
	ans.pb({{a,b},c});
}

void add_line(int i,int j) {
	point d=v[i]-v[j];
	d.y=-d.y;
	swap(d.x,d.y);
	ll a=d.x;
	ll b=d.y;
	ll c=v[i].x*v[j].y-v[j].x*v[i].y;
	ans.pb({{a,b},c});
}

bool is_center(int i) {
	int j=(i-1+n)%n;
	int k=(i+1)%n;
	point d1=v[j]-v[i];
	point d2=v[k]-v[i];
	return d1.x*d1.x+d1.y*d1.y==d2.x*d2.x+d2.y*d2.y;
}

void MAIN() {
	cin>>n;
	for(int i=0;i<n;i++) {
		cin>>v[i].x>>v[i].y;
	}
	v[n]=v[0];

	for(int i=0;i<n;i++) {
		int j=(i-1+n)%n;
		int k=(i+1)%n;
		a[2*i]={INF,INF};
		a[2*i+1]={(v[k]-v[i])*(v[k]-v[i]),(v[k]-v[i])/(v[k]-v[i])};
	}
	a[2*n]={INF,INF};

	manacher();

	map<pll,vector<int>> mp;
	pll a1={(v[2]-v[1])*(v[0]-v[1]),(v[2]-v[1])/(v[0]-v[1])};
	mp[a1]={1};

	for(int i=2;i<n;i++) {
		ans.clear();
		pll al={(v[1]-v[0])*(v[i]-v[0]),(v[1]-v[0])/(v[i]-v[0])};
		pll ar={(v[0]-v[i])*(v[i-1]-v[i]),(v[0]-v[i])/(v[i-1]-v[i])};
		pll ai={(v[i+1]-v[i])*(v[i-1]-v[i]),(v[i+1]-v[i])/(v[i-1]-v[i])};
		if(mp.count(al)) {
			vector<int>& lst=mp[al];
			for(int j:lst) {
				pll aj={(v[j+1]-v[j])*(v[j-1]-v[j]),(v[j+1]-v[j])/(v[j-1]-v[j])};
				if(ar==aj&&is_palindrome(0,j)&&(i==j+1||is_palindrome(j+2,i-1))) {
					if(j%2||is_center(j/2)) {
						add_perpen_line(0,j);
					}
				}
			}
		}
		if(ar==al&&is_palindrome(1,i-1)) {
			add_perpen_line(0,i);
		}
		if(ar==a1&&(i==2||is_palindrome(2,i-1))&&is_center(0)) {
			if(i%2)add_line(0,(i+1)/2);
			else add_perpen_line(i/2,i/2+1);
		}
		cout<<sz(ans)<<'\n';
		for(auto& it:ans) {
			cout<<it.fi.fi<<' '<<it.fi.se<<' '<<it.se<<'\n';
		}
		if(!mp.count(ai)) {
			mp[ai]={i};
		} else {
			mp[ai].pb(i);
		}
	}
}

int main() {
	ios::sync_with_stdio(false);cin.tie(0);

	int T;cin>>T;
	for(int tt=1;tt<=T;tt++) {
		MAIN();
	}
	return 0;
}