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;
const int maxn = 2e+5;
bool compare(double a, double b) { return fabs(a - b) < 1e-3; }
struct Line {
  double A, B, C;
  pair<double, double> f, s;
  Line() {}
  Line(pair<double, double> a, pair<double, double> b) {
    A = b.second - a.second;
    B = a.first - b.first;
    C = a.second * (b.first - a.first) - a.first * (b.second - a.second);
    f = a;
    s = b;
  }
  Line GetPerp() {
    Line answer;
    answer.A = -B;
    answer.B = A;
    pair<double, double> middle =
        make_pair(f.first + s.first, f.second + s.second);
    middle.first /= 2;
    middle.second /= 2;
    answer.C = -(answer.A * middle.first + answer.B * middle.second);
    return answer;
  }
  pair<double, double> Intersect(Line a) {
    double a11 = A;
    double a12 = B;
    double b1 = -C;
    double a21 = a.A;
    double a22 = a.B;
    double b2 = -a.C;
    double det = a11 * a22 - a12 * a21;
    if (compare(det, 0)) return make_pair(-1e+9, -1e+9);
    double det1 = b1 * a22 - a12 * b2;
    double det2 = a11 * b2 - b1 * a21;
    double x = det1 / det;
    double y = det2 / det;
    return make_pair(x, y);
  }
};
pair<double, double> a, b, c;
bool comparePoint(pair<double, double> a, pair<double, double> b) {
  if (fabs(a.first - b.first) < 1e-3)
    if (fabs(a.second - b.second) < 1e-3) return true;
  return false;
}
pair<double, double> FindCenter() {
  Line f(a, b);
  Line s(a, c);
  return (f.GetPerp()).Intersect(s.GetPerp());
}
double dist(pair<double, double> a, pair<double, double> b) {
  return pow((a.first - b.first) * (a.first - b.first) +
                 (a.second - b.second) * (a.second - b.second),
             0.5);
}
pair<double, double> rotate(pair<double, double> point, double angle) {
  pair<double, double> answer;
  answer.first = point.first * cos(angle) - point.second * sin(angle);
  answer.second = point.second * cos(angle) + point.first * sin(angle);
  return answer;
}
double ToRadian(double value) {
  double PI = 3.14159265358979;
  return value / 180 * PI;
}
bool model(int n) {
  int count = 0;
  pair<double, double> cur = a;
  for (int i = 0; i < n; i++) {
    cur = rotate(cur, ToRadian(360. / n));
    if (comparePoint(cur, a) || comparePoint(cur, b) || comparePoint(cur, c)) {
      count++;
    }
  }
  return count == 3;
  return true;
}
double solve() {
  double answer = 0;
  pair<double, double> cent = FindCenter();
  double dist1 = dist(cent, a);
  double dist2 = dist(cent, b);
  double dist3 = dist(cent, c);
  a.first -= cent.first;
  b.first -= cent.first;
  c.first -= cent.first;
  a.second -= cent.second;
  b.second -= cent.second;
  c.second -= cent.second;
  for (int i = 3; i <= 200; i++) {
    if (model(i)) {
      answer = i * (dist1 * dist1 * sin(ToRadian(360. / i))) / 2;
      break;
    }
  }
  return answer;
}
int main() {
  cin >> a.first >> a.second >> b.first >> b.second >> c.first >> c.second;
  cout << fixed << setprecision(15) << solve();
  return 0;
}