#include<bits/stdc++.h>
#define pb push_back
#define SZ(x) ((int)(x).size())
#define rep(i,a,b) for(int i=(a);i<=(b);++i)
#define per(i,a,b) for(int i=(a);i>=(b);--i)
using namespace std;
using LL=long long;
const int N=100005;
const LL INFLL=0X3F3F3F3F3F3F3F3FLL;
int T,n;
struct rec{
	LL x1,y1,x2,y2;
}a[N];
struct node{
	LL x,y;
	int op;
	bool operator<(const node&rhs)const{
		return tie(x,y)<tie(rhs.x,rhs.y);
	}
};
struct solver{
	vector<node>todo;
	void clear(){
		todo.clear();
	}
	void push(rec u,int op){
		todo.push_back((node){u.x1,u.y1,op});
		todo.push_back((node){u.x1,u.y2,-op});
		todo.push_back((node){u.x2,u.y1,-op});
		todo.push_back((node){u.x2,u.y2,op});
	}
	bool check(){
		sort(todo.begin(),todo.end());
		for(int i=0,j;i<SZ(todo);i=j){
			j=i;
			int s=0;
			while(j<SZ(todo)&&todo[i].x==todo[j].x&&todo[i].y==todo[j].y)s+=todo[j].op,++j;
			if(s!=0)return 0;
		}
		return 1;
	}
}A;

vector<tuple<LL,LL,LL> >ans;
int main(){
#ifdef xay5421
	freopen("a.in","r",stdin);
#endif
	cin>>T;
	while(T--){
		cin>>n;
		rep(i,1,n){
			cin>>a[i].x1>>a[i].y1>>a[i].x2>>a[i].y2;
		}
		ans.clear();
		{
			LL mn=INFLL,mx=-INFLL;
			rep(i,1,n){
				mn=min(mn,a[i].x1);
				mx=max(mx,a[i].x2);
			}
			A.clear();
			rep(i,1,n)A.push(a[i],1),A.push((rec){mn+mx-a[i].x2,a[i].y1,mn+mx-a[i].x1,a[i].y2},-1);
			if(A.check()){
				ans.emplace_back(2,0,mn+mx);
			}
		}
		{
			LL mn=INFLL,mx=-INFLL;
			rep(i,1,n){
				mn=min(mn,a[i].y1);
				mx=max(mx,a[i].y2);
			}
			A.clear();
			rep(i,1,n)A.push(a[i],1),A.push((rec){a[i].x1,mn+mx-a[i].y2,a[i].x2,mn+mx-a[i].y1},-1);
			if(A.check()){
				ans.emplace_back(0,2,mn+mx);
			}
		}
		{
			LL mn=INFLL,mx=-INFLL;
			rep(i,1,n){
				mn=min(mn,a[i].x1+a[i].y1);
				mx=max(mx,a[i].x2+a[i].y2);
			}
			A.clear();
			rep(i,1,n)A.push(a[i],1),A.push((rec){(mn+mx)*2-a[i].y2,(mn+mx)*2-a[i].x2,(mn+mx)*2-a[i].y1,(mn+mx)*2-a[i].x1},-1);
			if(A.check()){
				ans.emplace_back(2,2,mn+mx);
			}
		}
		{
		{
			LL mn=INFLL,mx=-INFLL;
			rep(i,1,n){
				mn=min(mn,a[i].x1-a[i].y2);
				mx=max(mx,a[i].x2-a[i].y1);
			}
			A.clear();
			rep(i,1,n)A.push(a[i],1),A.push((rec){(mn+mx)*2+a[i].y1,-(mn+mx)*2+a[i].x1,(mn+mx)*2+a[i].y2,-(mn+mx)*2+a[i].x2},-1);
			if(A.check()){
				ans.emplace_back(2,-2,mn+mx);
			}
		}
		}
		for(auto&x:ans){
			LL g=abs(__gcd(get<0>(x),__gcd(get<1>(x),get<2>(x))));
			get<0>(x)/=g,get<1>(x)/=g,get<2>(x)/=g;
		}
		sort(ans.rbegin(),ans.rend());
		printf("%d\n",SZ(ans));
		for(auto&x:ans){
			printf("%lld %lld %lld ",get<0>(x),get<1>(x),get<2>(x));
		}
		puts("");
		
	}
	return 0;
}