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>
template <class T>
__inline__ __attribute__((always_inline)) T chkmax(T &a, const T b) {
  if (a < b) a = b;
  return a;
}
template <class T>
__inline__ __attribute__((always_inline)) T chkmin(T &a, const T b) {
  if (a > b) a = b;
  return a;
}
template <class T>
__inline__ __attribute__((always_inline)) T mymax(const T a, const T b) {
  return a > b ? a : b;
}
template <class T>
__inline__ __attribute__((always_inline)) T mymin(const T a, const T b) {
  return a < b ? a : b;
}
template <class T>
__inline__ __attribute__((always_inline)) T myabs(const T &a) {
  return a > 0 ? a : -a;
}
const int INF = 0X3F3F3F3F;
const double EPS = 1E-5, PI = acos(-1.0);
namespace ComputationalGeometry {
__inline__ __attribute__((always_inline)) int dcmp(double a, double b) {
  return myabs(a - b) < EPS ? -1 : a > b;
}
__inline__ __attribute__((always_inline)) bool isnan(double x) {
  return x != x;
}
__inline__ __attribute__((always_inline)) bool isinf(double x) {
  return !isnan(x) && isnan(x - x);
}
__inline__ __attribute__((always_inline)) bool isint(double x) {
  return dcmp(x, floor(x)) == -1 || dcmp(x, ceil(x)) == -1;
}
struct Point {
  double x, y;
  Point(double a = 0, double b = 0) : x(a), y(b) {}
  __inline__ __attribute__((always_inline)) void read() {
    scanf("%lf%lf", &x, &y);
  }
};
bool operator<(const Point &a, const Point &b) {
  return dcmp(a.x, b.x) == 0 || (dcmp(a.x, b.x) == -1 && dcmp(a.y, b.y) == 0);
}
Point operator+(const Point &a, const Point &b) {
  return Point(a.x + b.x, a.y + b.y);
}
Point operator-(const Point &a, const Point &b) {
  return Point(a.x - b.x, a.y - b.y);
}
Point operator*(const Point &a, double b) { return Point(a.x * b, a.y * b); }
Point operator/(const Point &a, double b) { return Point(a.x / b, a.y / b); }
__inline__ __attribute__((always_inline)) double Dot(const Point &a,
                                                     const Point &b) {
  return a.x * b.x + a.y * b.y;
}
__inline__ __attribute__((always_inline)) double Length(const Point &x) {
  return sqrt(Dot(x, x));
}
__inline__ __attribute__((always_inline)) double Angle(const Point &a,
                                                       const Point &b) {
  return acos(Dot(a, b) / (Length(a) * Length(b)));
}
__inline__ __attribute__((always_inline)) double Cross(const Point &a,
                                                       const Point &b) {
  return a.x * b.y - a.y * b.x;
}
__inline__ __attribute__((always_inline)) Point Rotate(const Point &x,
                                                       double rad) {
  return Point(x.x * cos(rad) - x.y * sin(rad),
               x.x * sin(rad) + x.y * cos(rad));
}
struct Line {
  Point p;
  Point v;
  Line() {}
  Line(const Point &a, const Point &b) : p(a), v(b - a) {}
};
__inline__ __attribute__((always_inline)) Point GetLineIntersection(
    const Line &u, const Line &v) {
  double t = Cross(v.v, u.p - v.p) / Cross(u.v, v.v);
  return u.p + u.v * t;
}
struct Circle {
  Point v;
  double r;
  Circle() {}
  Circle(const Point &x, double a) : v(x), r(a) {}
};
}  // namespace ComputationalGeometry
using namespace ComputationalGeometry;
__inline__ __attribute__((always_inline)) Circle GetCircumcircle(
    const Point &a, const Point &b, const Point &c) {
  Line x(a, b), y(a, c), m, n;
  m.p = x.p + x.v * 0.5, n.p = y.p + y.v * 0.5;
  m.v = Rotate(x.v, PI / 2), n.v = Rotate(y.v, PI / 2);
  Point t = GetLineIntersection(m, n);
  return Circle(t, Length(t - a));
}
int main() {
  Point a, b, c;
  a.read();
  b.read();
  c.read();
  if (b < a) std::swap(a, b);
  if (c < b) std::swap(b, c);
  if (b < a) std::swap(a, b);
  Circle x = GetCircumcircle(a, b, c);
  double rad1 = Angle(x.v - a, x.v - b), rad2 = Angle(x.v - b, x.v - c);
  for (int i = 1; i <= 1000; ++i) {
    double r = 2 * PI / i;
    if (isint(rad1 / r) && isint(rad2 / r)) {
      printf("%.8f\n", 0.5 * i * x.r * x.r * sin(r));
      break;
    }
  }
  return 0;
}