// Ilie "The-Winner" Dumitru
#include <bits/stdc++.h>
using ll = long long;
const int NMAX=4005;
const double EPS=1e-6;
const ll MOD=1000000007;

// Linux
#ifdef ONLINE_JUDGE
#define lld "%I64d"
#else
#define lld "%lld"
#endif

struct el
{
	int r, g, b;
	double d;
};

std::vector<el> sol;

void solve(double r, double g, double b)
{
	if(fabs(r-g)<EPS && fabs(r-b)<EPS)
		sol.push_back({255, 255, 255, sqrt(3)*r});
	else
	{
		if(fabs(std::min(std::min(r, g), b))<EPS)
		{
			if(fabs(r)<EPS && fabs(g)<EPS)
				sol.push_back({0, 0, 255, b});
			else if(fabs(r)<EPS && fabs(b)<EPS)
				sol.push_back({0, 255, 0, g});
			else if(fabs(g)<EPS && fabs(b)<EPS)
				sol.push_back({255, 0, 0, r});
			else
			{
				double nr, ng, nb;
				int mr=255, mg=255, mb=255;

				if(fabs(r)<EPS)
				{
					nr=0;
					mr=0;
					if(g<b)
					{
						double s=(255-b)/(255-g);
						nb=b-s*g;
						ng=0;
					}
					else
					{
						double s=(255-g)/(255-b);
						ng=g-s*b;
						nb=0;
					}
				}
				else if(fabs(g)<EPS)
				{
					ng=0;
					mg=0;
					if(r<b)
					{
						double s=(255-b)/(255-r);
						nb=b-s*r;
						nr=0;
					}
					else
					{
						double s=(255-r)/(255-b);
						nr=r-s*b;
						nb=0;
					}
				}
				else
				{
					nb=0;
					mb=0;
					if(g<r)
					{
						double s=(255-r)/(255-g);
						nr=r-s*g;
						ng=0;
					}
					else
					{
						double s=(255-g)/(255-r);
						ng=g-s*r;
						nr=0;
					}
				}

				solve(nr, ng, nb);
				sol.push_back({mr, mg, mb, sqrt((nr-r)*(nr-r)+(ng-g)*(ng-g)+(nb-b)*(nb-b))});
			}
		}
		else
		{
			double nr, ng, nb, c, min=std::min(r, std::min(g, b)), d;

			c=min/(255-min);

			nr=r-255;
			ng=g-255;
			nb=b-255;
			d=sqrt(nr*nr+ng*ng+nb*nb);

			nr=r+c*nr;
			ng=g+c*ng;
			nb=b+c*nb;

			solve(nr, ng, nb);
			sol.push_back({255, 255, 255, c*d});
		}
	}
}

void solve()
{
	int r, g, b;

	scanf("%d%d%d", &r, &g, &b);
	sol.clear();
	solve(r, g, b);
	printf("%d\n", (int)sol.size());
	for(el e : sol)
		printf("%d %d %d %.9f\n", e.r, e.g, e.b, e.d);
}

int main()
{
	int _=1;

	scanf("%d", &_);
	do solve(); while(--_);

    return 0;
}