#include <bits/stdc++.h>
using namespace std;
#define FOR(i,k,n) for(int i = (int)(k); i < (int)(n); i++)
#define REP(i,n) FOR(i,0,n)
#define ALL(a) a.begin(), a.end()
#define MS(m,v) memset(m,v,sizeof(m))
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<string> vs;
typedef pair<int, int> pii;
const int MOD = 1e9 + 7;
template<class T> T &chmin(T &a, const T &b) { return a = min(a, b); }
template<class T> T &chmax(T &a, const T &b) { return a = max(a, b); }
template<class T>
istream& operator >> (istream& is, vector<T>& v)
{
	for (auto &i : v) is >> i;
	return is;
}
template<class T>
ostream& operator<<(ostream& os, vector<T>& v)
{
	const string delimiter = "\n";
	REP(i, v.size())
	{
		os << v[i];
		if (i != v.size() - 1) os << delimiter;
	}
	return os;
}
/*--------------------template--------------------*/

typedef long double ld;
const ld EPS = 1e-12;
const ld PI = acos(-1.0);
bool eq(ld a, ld b) { return abs(a - b) < EPS; }
typedef complex<ld> Point;
typedef vector<Point> Polygon;

namespace std
{
	bool operator < (const Point& a, const Point& b)
	{
		return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
	}
}

struct Line
{
	Point a, b;
	Line() {};
	Line(Point p, Point q) :a(p), b(q) {};
	Line(ld x1, ld y1, ld x2, ld y2) :a(Point(x1, y1)), b(Point(x2, y2)) {};
};

struct Circle
{
	Point p; ld r;
	Circle() {};
	Circle(Point a, ld b) :p(a), r(b) {};
};

ld dot(Point a, Point b)
{
	return real(conj(a)*b);
}

ld cross(Point a, Point b)
{
	return imag(conj(a)*b);
}

int ccw(Point a, Point b, Point c)
{
	b -= a; c -= a;
	if (cross(b, c) > EPS) return 1;    //counter cloclwise
	if (cross(b, c) < -EPS) return -1;  //cloclwise
	if (dot(b, c) < 0) return 2;        //c--a--b on line 
	if (norm(b) < norm(c)) return -2;   //a--b--c on line
	return 0;                           //a--c--b on line
}

bool isis_ll(Line l, Line m)
{
	return abs(cross(l.b - l.a, m.b - m.a)) > EPS;
}

bool isis_ls(Line l, Line s)
{
	return cross(l.b - l.a, s.a - l.a)*cross(l.b - l.a, s.b - l.a) < EPS;
}

bool isis_ss(Line s, Line t)
{
	return (ccw(s.a, s.b, t.a)*ccw(s.a, s.b, t.b) <= 0 &&
		ccw(t.a, t.b, s.a)*ccw(t.a, t.b, s.b) <= 0);
}

bool isis_lp(Line l, Point p)
{
	return (abs(cross(l.b - p, l.a - p)) < EPS);
}

bool isis_sp(Line s, Point p)
{
	return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a)) < EPS;
}

Point projection(Line l, Point p)
{
	Point base = l.b - l.a;
	ld r = dot(p - l.a, base) / norm(base);
	return l.a + base*r;
}

Point mirror(Line l, Point p)
{
	return Point(2, 0)*projection(l, p) - p;
}

ld dist_lp(Line l, Point p)
{
	return abs(p - projection(l, p));
}

ld dist_ll(Line l, Line m)
{
	return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(Line l, Line s)
{
	if (isis_ls(l, s)) return 0;
	return min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p)
{
	Point r = projection(s, p);
	if (isis_sp(s, r)) return abs(r - p);
	return min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t)
{
	if (isis_ss(s, t)) return 0;
	return min(min(dist_sp(s, t.a), dist_sp(s, t.b)), min(dist_sp(t, s.a), dist_sp(t, s.b)));
}

Point is_ll(Line s, Line t)
{
	ld a = cross(s.b - s.a, t.b - t.a);
	ld b = cross(s.b - s.a, s.b - t.a);
	return t.a + b / a*(t.b - t.a);
}

vector<Point> is_cc(Circle c1, Circle c2)
{
	vector<Point> res;
	ld d = abs(c1.p - c2.p);
	ld rc = (d*d + pow(c1.r, 2) - pow(c2.r, 2)) / (2 * d);
	ld dfr = pow(c1.r, 2) - rc*rc;
	if (abs(dfr) < EPS) dfr = 0;
	if (dfr < 0.0) return res;
	ld rs = sqrt(dfr);
	Point diff = (c2.p - c1.p) / d;
	res.push_back(c1.p + diff*Point(rc, rs));
	if (dfr != 0.0) res.push_back(c1.p + diff*Point(rc, -rs));
	return res;
}

int isis_cc(Circle c1, Circle c2)
{
	ld d = abs(c1.p - c2.p);
	if (d - c1.r - c2.r > EPS) return -2; //separate
	if (abs(d - c1.r - c2.r) < EPS) return -1; //circumscribe
	if (c1.r < c2.r) swap(c1, c2);
	if (abs(d - c1.r + c2.r) < EPS) return 1;//inscribe
	if (c1.r - d - c2.r > EPS) return 2;//involve
	else return 0;//intersect
}

bool isis_cl(Circle c, Line l)
{
	ld d = dist_lp(l, c.p);
	return d - c.r < -EPS;
}

vector<Point> is_cl(Circle c, Line l)
{
	vector<Point> res;
	ld d = dist_lp(l, c.p);
	if (d > c.r + EPS) return res;
	ld len = (d > c.r) ? 0 : sqrt(c.r*c.r - d*d);
	Point nor = (l.a - l.b) / abs(l.a - l.b);
	res.push_back(projection(l, c.p) + len*nor);
	if (abs(len) > EPS) res.push_back(projection(l, c.p - len*nor));
	return res;
}

vector<Point> is_cs(Circle c, Line s)
{
	vector<Point> v = is_cl(c, s), res;
	REP(i, v.size())
	{
		if (ccw(s.a, v[i], s.b) == -2) res.push_back(v[i]);
	}
	return res;
}

vector<Line> tangent_cp(Circle c, Point p)
{
	vector<Line> res;
	Point v = c.p - p;
	ld d = abs(v);
	ld l = sqrt(norm(v) - c.r * c.r);
	if (isnan(l)) { return res; }
	Point v1 = v * Point(l / d, c.r / d);
	Point v2 = v * Point(l / d, -c.r / d);
	res.push_back(Line(p, p + v1));
	if (l < EPS) return res;
	res.push_back(Line(p, p + v2));
	return res;
}

vector<Line> tangent_cc(Circle c1, Circle c2)
{
	vector<Line> res;
	if (abs(c1.p - c2.p) - (c1.r + c2.r) > -EPS)
	{
		Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
		res = tangent_cp(c1, center);
	}
	if (abs(c1.r - c2.r) > EPS)
	{
		Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
		vector<Line> nres = tangent_cp(c1, out);
		res.insert(res.end(), nres.begin(), nres.end());
	}
	else
	{
		Point v = c2.p - c1.p; v /= abs(v);
		Point q1 = c1.p + v * Point(0, 1) * c1.r;
		Point q2 = c1.p + v * Point(0, -1) * c1.r;
		res.push_back(Line(q1, q1 + v));
		res.push_back(Line(q2, q2 + v));
	}
	return res;
}

Polygon ConvexCut(const Polygon& g, const Line l)
{
	Polygon res;
	REP(i, g.size())
	{
		Point a = g[i], b = g[(i + 1) % g.size()];
		if (ccw(l.a, l.b, a) != -1) res.push_back(a);
		if (ccw(l.a, l.b, a)*ccw(l.a, l.b, b) < 0) res.push_back(is_ll(Line(a, b), l));
	}
	return res;
}

ld area(const Polygon &p) {
	ld res = 0;
	int n = p.size();
	REP(j, n) res += cross(p[j], p[(j + 1) % n]);
	return res / 2;
}

int main()
{
	cin.sync_with_stdio(false); cout << fixed << setprecision(10);

	int cs = 1;
	Polygon g{ Point(0, 0), Point(10000, 0), Point(10000,10000), Point(0, 10000) };
	ld a, b, c, d, e, f;

	while (cin >> a >> b >> c >> d >> e >> f)
	{
		if (a == 0 && b == 0 && c == 0 && d == 0 && e == 0 && f == 0) break;
		vector<Point> ps = { Point(a, b), Point(c,d), Point(e,f) };

		Polygon t = g;
		vector<Line> ls;
		FOR(i, 1, 3)
		{
			Line a(ps[0], ps[i]);
			Point v(-(a.b.imag() - a.a.imag()), a.b.real() - a.a.real());
			Point m = (a.a + a.b) / Point(2, 0);
			ls.emplace_back(Line(m, m + v));

		}
		for (auto l : ls)
		{
			if (ccw(l.a, l.b, ps[0]) < 0) swap(l.a, l.b);
			t = ConvexCut(t, l);
		}
		cout << cs << " " << area(t) / ld(10000 * 10000) << endl;
		cs++;
	}
	return 0;
}

Measured memory_bytes: 3288