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

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); i--)
#define SZ(a) int(a.size())
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first
#define S second

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

const int mod1 = 1e9 + 7;
const int mod2 = 1e9 + 9;
const LL mod = (LL)mod1 * mod2;
const int C = 1e8 + 47;
const int INF = 1e9;
const LL p = 892388953;
const LL q = 347723788;

LL add(LL a, LL b)
{
	return a + b < mod ? a + b : a + b - mod;
}

LL sub(LL a, LL b)
{
	return a - b >= 0 ? a - b : a - b + mod;
}

LL mult(LL a, LL b)
{
	return (__int128)a * b % mod;
}

LL binpow(LL a, int n)
{
	LL res = 1;
	while (n)
	{
		if (n & 1)
			res = mult(res, a);
		a = mult(a, a);
		n >>= 1;
	}
	return res;
}

LL getRectHash(int x1, int y1, int x2, int y2)
{
	if (x1 > x2)
		swap(x1, x2);
	if (y1 > y2)
		swap(y1, y2);
	return mult(sub(binpow(p, x2 + C), binpow(p, x1 + C)), sub(binpow(q, y2 + C), binpow(q, y1 + C)));
}

pair<bool, PII> reflect(LL a, LL b, LL c, LL x, LL y)
{
	LL num1 = 2 * a * (a * x + b * y + c), num2 = 2 * b * (a * x + b * y + c);
	LL den = a * a + b * b;
	if (num1 % den != 0 || num2 % den != 0)
	{
		return {false, {0, 0}};
	}
	return {true, {x - num1 / den, y - num2 / den}};
}

void solve()
{
	int n;
	cin >> n;
	VI x1(n), y1(n), x2(n), y2(n);
	FOR(i, 0, n)
	{
		cin >> x1[i] >> y1[i] >> x2[i] >> y2[i];
	}
	LL h0 = 0;
	FOR(i, 0, n)
	{
		h0 = add(h0, getRectHash(x1[i], y1[i], x2[i], y2[i]));
	}
	auto check = [&](int a, int b, int c) -> bool
	{
		LL h = 0;
		FOR(i, 0, n)
		{
			auto [can1, p1] = reflect(a, b, c, x1[i], y1[i]);
			auto [can2, p2] = reflect(a, b, c, x2[i], y2[i]);
			if (!can1 || !can2)
				return false;
			h = add(h, getRectHash(p1.F, p1.S, p2.F, p2.S));
		}
		return h == h0;
	};
	vector<tuple<int, int, int>> ans;
	auto f = [&](int a, int b) -> void
	{
		int mn = INF, mx = -INF;
		FOR(i, 0, n)
		{
			mn = min(mn, a * x1[i] + b * y1[i]);
			mn = min(mn, a * x1[i] + b * y2[i]);
			mn = min(mn, a * x2[i] + b * y1[i]);
			mn = min(mn, a * x2[i] + b * y2[i]);
			
			mx = max(mx, a * x1[i] + b * y1[i]);
			mx = max(mx, a * x1[i] + b * y2[i]);
			mx = max(mx, a * x2[i] + b * y1[i]);
			mx = max(mx, a * x2[i] + b * y2[i]);
		}
		int c = (mn + mx) / 2;
		if (check(a, b, c))
		{
			ans.PB({a, b, c});
		}
	};
	f(0, 2);
	f(2, 0);
	f(2, 2);
	f(2, -2);
	for (auto& [a, b, c] : ans)
	{
		int g = gcd(gcd(abs(a), abs(b)), abs(c));
		a /= g;
		b /= g;
		c /= g;
	}
	sort(ALL(ans), greater());
	cout << SZ(ans) << "\n";
	FOR(i, 0, SZ(ans))
	{
		auto [a, b, c] = ans[i];
		if (i > 0)
			cout << " ";
		cout << a << " " << b << " " << c;
	}
	cout << "\n";
}

int main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	int t;
	cin >> t;
	while (t--)
	{
		solve();
	}
	return 0;
}
fghjkl

answer.code:158:1: error: ‘fghjkl’ does not name a type
  158 | fghjkl
      | ^~~~~~