Problem: Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.

In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.

Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.

You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.

Input

The input file consists of three lines, each of them contains a pair of numbers –– coordinates of the pillar. Any coordinate doesn't exceed 1000 by absolute value, and is given with at most six digits after decimal point.

Output

Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It's guaranteed that the number of angles in the optimal polygon is not larger than 100.

Examples

Input

0.000000 0.000000
1.000000 1.000000
0.000000 1.000000


Output

1.00000000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
inline int cmp(long double x, long double y = 0, long double tol = 1e-5) {
  return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1;
}
struct ponto {
  double x, y;
  ponto() : x(0), y(0) {}
  ponto(double x, double y) : x(x), y(y) {}
  bool operator<(const ponto outro) const {
    if (fabs(x - outro.x) > 1e-5) return x < outro.x;
    return y < outro.y;
  }
  bool operator==(const ponto outro) const {
    return (fabs(x - outro.x) < 1e-5 && (fabs(y - outro.y)) < 1e-5);
  }
};
ponto rotate(ponto p, double theta) {
  double rad = (2 * acos(0) * theta / 180.0);
  return ponto(p.x * cos(rad) - p.y * sin(rad),
               p.x * sin(rad) + p.y * cos(rad));
}
double dist(ponto p1, ponto p2) { return hypot(p1.x - p2.x, p1.y - p2.y); }
struct linha {
  double a, b, c;
};
void FazLinha(ponto p1, ponto p2, linha &l) {
  if (fabs(p1.x - p2.x) < 1e-5) {
    l.a = 1.0;
    l.b = 0.0;
    l.c = -p1.x;
  } else {
    l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x);
    l.b = 1.0;
    l.c = -(double)(l.a * p1.x) - p1.y;
  }
}
bool Paralelas(linha l1, linha l2) {
  return (fabs(l1.a - l2.a) < 1e-5) && fabs(l1.b - l2.b) < 1e-5;
}
bool Iguais(linha l1, linha l2) {
  return Paralelas(l1, l2) && (fabs(l1.c - l2.c) < 1e-5);
}
bool Intersecao(linha l1, linha l2, ponto &p) {
  if (Paralelas(l1, l2)) return false;
  p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);
  if (fabs(l1.b) > 1e-5)
    p.y = -(l1.a * p.x + l1.c);
  else
    p.y = -(l2.a * p.x + l2.c);
  return true;
}
struct vetor {
  double x, y;
  vetor(double x, double y) : x(x), y(y) {}
};
vetor FazVetor(ponto a, ponto b) { return vetor(b.x - a.x, b.y - a.y); }
vetor scale(vetor v, double s) { return vetor(v.x * s, v.y * s); }
ponto translate(ponto p, vetor v) { return ponto(p.x + v.x, p.y + v.y); }
double dot(vetor a, vetor b) { return (a.x * b.x + a.y * b.y); }
double ModuloVetor_semRaiz(vetor v) { return v.x * v.x + v.y * v.y; }
double distToline(ponto p, ponto a, ponto b, ponto &c) {
  vetor ap = FazVetor(a, p);
  vetor ab = FazVetor(a, b);
  double u = dot(ap, ab) / ModuloVetor_semRaiz(ab);
  c = translate(a, scale(ab, u));
  return dist(p, c);
}
double distTolineSegment(ponto p, ponto a, ponto b, ponto &c) {
  vetor ap = FazVetor(a, p);
  vetor ab = FazVetor(a, b);
  double u = dot(ap, ab) / ModuloVetor_semRaiz(ab);
  if (u < 0.0) {
    c = ponto(a.x, a.y);
    return dist(p, a);
  }
  if (u > 1.0) {
    c = ponto(b.x, b.y);
    return dist(p, b);
  }
  return distToline(p, a, b, c);
}
double angle(ponto a, ponto o, ponto b) {
  vetor oa = FazVetor(o, a);
  vetor ob = FazVetor(o, b);
  return acos(dot(oa, ob) /
              sqrt(ModuloVetor_semRaiz(oa) * ModuloVetor_semRaiz(ob)));
}
double cross(vetor a, vetor b) { return a.x * b.y - a.y * b.x; }
bool ccw(ponto p, ponto q, ponto r) {
  return cross(FazVetor(p, q), FazVetor(p, r)) > 0;
}
bool collinear(ponto p, ponto q, ponto r) {
  return fabs(cross(FazVetor(p, q), FazVetor(p, r))) < 1e-5;
}
int det3pontos_ori(ponto p, ponto a, ponto b) {
  double det = ((-(p.x * b.y) - (b.x * a.y) - (a.x * p.y)) + (p.y * b.x) +
                (a.y * p.x) + (b.y * a.x));
  return fabs(det) < 1e-5 ? 0 : det > 0 ? 1 : -1;
}
bool collinear_det(ponto a, ponto b, ponto c) {
  return ((b.y - a.y) * (c.x - b.x) == (b.x - a.x) * (c.y - b.y));
}
inline bool le(ponto &p) {
  if (cin >> p.x >> p.y) return true;
  return false;
}
inline void imprime(ponto p) { cout << p.x << " " << p.y; }
double cross(ponto origem, ponto a, ponto b) {
  return (a.x - origem.x) * (b.y - origem.y) -
         (a.y - origem.y) * (b.x - origem.x);
}
double Area(double mediana1, double mediana2, double mediana3) {
  double sm = (mediana1 + mediana2 + mediana3) / 2.0;
  double temp = sm * (sm - mediana1) * (sm - mediana2) * (sm - mediana3);
  if (0 >= temp)
    return -1;
  else
    return 4.0 * sqrt(temp) / 3.0;
}
bool ValidaTriangulo(double l1, double l2, double l3) {
  return cmp(l1, abs(l3 - l2) > 0 && cmp((l3 + l2), l1) > 0 &&
                     cmp(l2, abs(l1 - l3)) > 0 && cmp((l1 + l3), l2) > 0 &&
                     cmp(l3, abs(l2 - l1)) > 0 && cmp((l2 + l1), l3)) > 0;
}
void linhaperpendicular(linha l, ponto p, linha &l1) {
  if (fabs(l.a) < 1e-5) {
    l1.a = 1.0;
    l1.b = 0.0;
    l1.c = -p.x;
    return;
  }
  l1.a = -l.b / l.a;
  l1.b = 1.0;
  l1.c = (double)-p.y + (l.b * p.x) / l.a;
}
ponto pontomedio(ponto a, ponto b) {
  return ponto((a.x + b.x) / 2.0, (a.y + b.y) / 2.0);
}
double det2pontos(vetor a, vetor b) { return ((a.x * b.y) - (b.x * a.y)); }
ponto sum(ponto a, ponto b) { return ponto(a.x + b.x, a.y + b.y); }
void AchaCentroCircunferencia3Pontos(ponto a, ponto b, ponto c, ponto &CENTRO) {
  linha l1, l2, l3, l4;
  FazLinha(a, b, l1);
  FazLinha(c, a, l2);
  linhaperpendicular(l1, pontomedio(a, b), l3);
  linhaperpendicular(l2, pontomedio(c, a), l4);
  Intersecao(l3, l4, CENTRO);
}
int main() {
  cin.sync_with_stdio(0), cin.tie(0);
  cout << setprecision(10) << fixed;
  vector<ponto> v(3);
  le(v[0]), le(v[1]), le(v[2]);
  ponto c;
  double ans = 1e15;
  AchaCentroCircunferencia3Pontos(v[0], v[1], v[2], c);
  double r = dist(c, v[0]);
  for (int n = 3; n < 100000; ++n) {
    double theta = 360. / n;
    ponto p = v[0];
    bool o1 = 0, o2 = 0;
    for (int i = 1; i <= n; ++i) {
      if (p == v[1]) o1 = 1;
      if (p == v[2]) o2 = 1;
      p = sum(rotate(ponto(p.x - c.x, p.y - c.y), theta), c);
    }
    if (o1 && o2) {
      double b = sin((2 * acos(0) * theta / 2. / 180.0)) * r * 2;
      double h = cos((2 * acos(0) * theta / 2 / 180.0)) * r;
      cout << b * h / 2. * n << '\n';
      return 0;
    }
  }
  cout << ans << endl;
  return 0;
}