Problem: There is a flat island whose shape is a perfect square. On this island, there are three habitants whose names are IC, PC, and ACM Every day, one jewel is dropped from the heaven. Just as the jewel touches the ground, IC, PC, and ACM leave their houses simultaneously, run with the same speed, and then a person who first touched the jewel can get the jewel. Hence, the person whose house is nearest to the location of the jewel is the winner of that day.

They always have a quarrel with each other, and therefore their houses are located at distinct places. The locations of their houses are fixed. This jewel falls at a random point on the island, that is, all points on the island have even chance.

When three are two or more persons whose houses are simultaneously nearest, the last person in the order of

IC, PC, ACM

obtains the jewel.

Our interest is to know the probability for IC to get the jewel under this situation.



Input

The input describes one problem instance per line. Each line contains the x- and y-coordinates of IC's home, those of PC's, and those of ACM's in this order. Note that the houses of IC, PC and ACM are located at distinct places. The end of the input is indicated by a line with six zeros.

The coordinates of the whole island are given by (0, 10000) × (0, 10000) and coordinates of houses are given in integer numbers between 1 and 9999, inclusive. It should be noted that the locations of the jewels are arbitrary places on the island and their coordinate values are not necessarily integers.

Output

For each input line, your program should output its sequence number starting from 1, and the probability for the instance. The computed probability values should have errors less than 10-5.

The sequence number and the probability should be printed on the same line. The two numbers should be separated by a space.

Example

Input

2000 2000 8000 8000 9000 9500
2500 2500 7500 2500 2500 7500
0 0 0 0 0 0


Output

1 0.50000
2 0.25000

Solution (in CPP):

Solution:
#include <iostream>
#include <sstream>
#include <string>
#include <algorithm>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <cassert>

using namespace std;

#define FOR(i,k,n) for(int i=(k); i<(int)(n); ++i)
#define REP(i,n) FOR(i,0,n)
#define FORIT(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)

template<class T> void debug(T begin, T end){ for(T i = begin; i != end; ++i) cerr<<*i<<" "; cerr<<endl; }
inline bool valid(int x, int y, int W, int H){ return (x >= 0 && y >= 0 && x < W && y < H); }

typedef long long ll;
const int INF = 100000000;
const double EPS = 1e-8;
const int MOD = 1000000007;
int dx[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int sign(double r){ return (r < -EPS) ? -1 : (r > EPS) ? 1 : 0; }
bool eq(double a, double b){ return abs(b - a) < EPS; }

struct Point{
  double x, y;
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point operator+(const Point& b) const { return Point(x + b.x, y + b.y); }
  Point operator-(const Point& b) const { return Point(x - b.x, y - b.y); }
  Point operator*(const double b) const { return Point(x * b, y * b); }
  Point operator*(const Point& b) const { return Point(x * b.x - y * b.y, x * b.y + y * b.x); }
  Point operator/(const double b) const { return Point(x / b, y / b); }
  bool operator< (const Point& b) const { return x != b.x ? x < b.x : y < b.y; }
  bool operator==(const Point& b) const { return eq(x, b.x) && eq(y, b.y); }
  double norm(){ return x * x + y * y; }
  double arg(){ return atan2(x, y); }
  double abs(){ return sqrt(norm()); }
  Point rotate(double theta){ return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y); }
  Point rotate90(){ return Point(-y, x); }
};

ostream& operator<<(ostream& os, Point& p){ return os<<"("<<p.x<<","<<p.y<<")"; }
istream& operator>>(istream& is, Point& a){ return is>>a.x>>a.y; }
double dot(const Point& a, const Point& b){ return a.x * b.x + a.y * b.y; }
double cross(const Point& a, const Point& b){ return a.x * b.y - a.y * b.x; }
Point polor(double rho, double theta){ return Point(rho * cos(theta), rho * sin(theta)); }

struct Line : public vector<Point> {
  Line(const Point& a, const Point& b) {
    push_back(a); push_back(b);
  }
  Point vector() const {
    return back() - front();
  }
};
struct Circle : Point {
  double r;
  Circle(Point p, double r) : Point(p), r(r) { }
};
typedef vector<Point> Polygon;
Point curr(const Polygon& a, int x){ return a[x]; }
Point next(const Polygon& a, int x){ return a[(x + 1) % a.size()]; }
Point prev(const Polygon& a, int x){ return a[(x - 1 + a.size()) % a.size()]; }

//a->b->c
int ccw(Point a, Point b, Point c) {
  b = b - a; c = c - a;
  if (cross(b, c) > EPS)   return +1; // 反時計回り
  if (cross(b, c) < -EPS)   return -1; // 時計回り
  if (dot(b, c) < 0)     return +2; // c--a--b の順番で一直線上
  if (b.norm() < c.norm()) return -2; // a--b--c の順番で一直線上
  return 0;                         // a--c--b の順番で一直線上 (aがbまたはcと重なる場合を含む)
}
// 二直線の交差判定
bool intersectLL(const Line& l, const Line& m) {
  // 直線lと直線mが平行でない
  return abs(cross(l.vector(), m.vector())) > EPS;
}
// 二直線の同一判定
bool equalLL(const Line& l, const Line& m){
  // 直線lとl[0]からm[0]への直線が並行
  return abs(cross(l.vector(), m[0] - l[0])) < EPS;
}
// 直線と線分の交差判定(注意: 同一直線上にある場合も含む)
bool intersectLS(const Line& l, const Line& s) {
  // 直線lについて、線分sの端点が異なる側にある
  return cross(l.vector(), s[0] - l[0]) * cross(l.vector(), s[1] - l[0]) < EPS; 
}
// 直線と点の交差判定
bool intersectLP(const Line& l, const Point& p) {
  // 直線lとl[0]からpへの直線が平行
  return abs(cross(l.vector(), p - l[0])) < EPS;
}
// 二つの線分の交差判定
bool intersectSS(const Line& s, const Line& t) {
  return ccw(s[0], s[1], t[0]) * ccw(s[0], s[1], t[1]) <= 0 &&
         ccw(t[0], t[1], s[0]) * ccw(t[0], t[1], s[1]) <= 0;
}
// 線分と点の交差判定(端点を含む)
bool intersectSP(const Line& s, const Point& p) {
  return ccw(s[0], s[1], p) == 0;
}
// 円と点の交差判定(EPS注意)
bool intersectCP(const Circle& c, const Point& p){
  // 円の中心と点の距離が、円の半径以下である
  return (c - p).abs() < c.r + EPS;
}
// 二つの円の交差判定(EPS注意)
bool intersectCC(const Circle& c, const Circle& d){
  // 円の中心同士の距離が、半径の和以下であり、半径の差以上である
  return (c - d).abs() < c.r + d.r + EPS && (c - d).abs() > abs(c.r - d.r) - EPS;
}
// 射影
Point projection(const Line& l, const Point& p){
  double t = dot(p - l[0], l.vector()) / l.vector().norm();
  return l[0] + l.vector() * t;
}
// 反射
Point reflection(const Line& l, const Point& p){
  return p + (projection(l, p) - p) * 2;
}
// 直線と点の距離
double distanceLP(const Line& l, const Point& p){
  // pからlに下ろした垂線の長さ
  return (p - projection(l, p)).abs();
}
// 二直線の距離
double distanceLL(const Line& l, const Line& m){
  // 平行でないときは0, 平行のときは垂線の長さ
  return intersectLL(l, m) ? 0 : distanceLP(l, m[0]);
}
// 直線と線分の距離
double distanceLS(const Line& l, const Line& s){
  if(intersectLS(l, s)) return 0;
  return min(distanceLP(l, s[0]), distanceLP(l, s[1]));
}
// 線分と点の距離
double distanceSP(const Line& s, const Point& p){
  const Point r = projection(s, p);
  if(intersectSP(s, r)) return (r - p).abs(); // 垂線が線分に交わるとき
  return min((s[0] - p).abs(), (s[1] - p).abs());
}
// 二つの線分の距離
double distanceSS(const Line& s, const Line& t){
  if(intersectSS(s, t)) return 0;
  return min(min(distanceSP(s, t[0]), distanceSP(s, t[1])),
             min(distanceSP(t, s[0]), distanceSP(t, s[1])));
}
// 二直線の交点
Point crosspointLL(const Line& l, const Line& m){
  double d = cross(m.vector(), l.vector());
  if(abs(d) < EPS) assert(false); // 直線が交わらない
  return l[0] + l.vector() * cross(m.vector(), m[1] - l[0]) * (1.0 / d);
}

// 点が多角形のどこにあるのか判定する
enum { OUT, ON, IN };
int contains(const Polygon& P, const Point& p){
  // 点pから半直線をひき、辺と交差する回数を数える
  bool in = false;
  REP(i, P.size()){
    Point a = curr(P, i) - p;
    Point b = next(P, i) - p;
    if(a.y > b.y) swap(a, b);
    // aからbの直線がy=0と交わり、その交点は原点の右側である
    if(a.y <= 0 && 0 < b.y && cross(a, b) < 0){ 
      in = !in;
    }
    if(cross(a, b) == 0 && dot(a, b) <= 0) return ON;
  }
  return in ? IN : OUT;
}

// 多角形の面積
double area(const Polygon& P) {
  double A = 0;
  REP(i, P.size()){
    A += cross(curr(P, i), next(P, i));
  }
  return A / 2.0;
}

// 凸多角形の直線による切断。直線の左側だけ残す
Polygon convex_cut(const Polygon& P, const Line& l){
  Polygon Q;
  REP(i, P.size()){
    Point A = curr(P, i), B = next(P, i);
    if(ccw(l[0], l[1], A) != -1) Q.push_back(A); //Aが直線lの右側でない
    if(ccw(l[0], l[1], A) * ccw(l[0], l[1], B) < 0)
      Q.push_back(crosspointLL(l, Line(A, B)));
  }
  return Q;
}
// 垂直二等分線
Line bisector(const Point& a, const Point& b){
  Point mid = (a + b) / 2.0;
  Point vec = (mid - a).rotate90();
  return Line(mid, mid + vec);
}
// 点集合psのうちs番目のボロノイ領域
Polygon voronoi_cell(Polygon P, const vector<Point>& ps, int s){
  REP(i, ps.size())if(i != s){
    P = convex_cut(P, bisector(ps[s], ps[i]));
  }
  return P;
}
int main(){
  int C = 1;
  while(true){
    int N = 3;
    vector<Point> ps(N);
    REP(i, N) cin >> ps[i];
    if(ps[0] == Point(0, 0)) break;
    Polygon Field;
    Field.push_back(Point(0, 0));
    Field.push_back(Point(10000, 0));
    Field.push_back(Point(10000, 10000));
    Field.push_back(Point(0, 10000));
    Polygon obtain = voronoi_cell(Field, ps, 0);
    double ans = area(obtain) / 1e8;
    printf("%d ", C++);
    printf("%.8f\n", ans);
  }
  return 0;
}