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 INF = 1000 * 1000 * 1000 + 7;
const double EPS = 3e-5;
int bit_count(int first) {
  return first == 0 ? 0 : 1 + bit_count(first & (first - 1));
}
inline int last_bit(int first) { return first & -first; }
inline int sign(double first) {
  return first < -EPS ? -1 : first > EPS ? 1 : 0;
}
inline int sign(int first) { return (first > 0) - (first < 0); }
int nextComb(int first) {
  int smallest = first & -first;
  int ripple = first + smallest;
  int ones = first ^ ripple;
  ones = (ones >> 2) / smallest;
  return ripple | ones;
}
int gcd(int a, int b) {
  while (b) {
    int r = a % b;
    a = b;
    b = r;
  }
  return a;
}
int lcm(int a, int b) { return a / gcd(a, b) * b; }
struct UnionFind {
  vector<int> P, S, R;
  UnionFind(int n)
      : P(vector<int>(n)), S(vector<int>(n, 1)), R(vector<int>(n, 1)) {
    for (int i = (int)0; i < (int)n; ++i) P[i] = i;
  }
  int findP(int first) {
    if (P[first] != first) P[first] = findP(P[first]);
    return P[first];
  }
  inline int operator[](const int first) { return findP(first); }
  int merge(int a, int b) {
    int pa = findP(a), push_back = findP(b);
    if (pa == push_back) return 0;
    if (R[pa] < R[push_back]) {
      P[pa] = push_back;
      S[push_back] += S[pa];
    } else {
      P[push_back] = pa;
      S[pa] += S[push_back];
    }
    if (R[pa] == R[push_back]) ++R[pa];
    return 1;
  }
};
const int BUF_SIZE = 201;
char buf[BUF_SIZE];
inline string getToken() {
  scanf("%s", buf);
  return buf;
}
inline string getLine() {
  fgets(buf, BUF_SIZE, stdin);
  return buf;
}
inline int getInt() {
  int a;
  scanf("%d", &a);
  return a;
}
inline double getDouble() {
  double a;
  scanf("%lf", &a);
  return a;
}
inline int stoi(string first) {
  stringstream ss;
  int ret;
  ss << first;
  ss >> ret;
  return ret;
}
inline vector<string> split(string &s) {
  stringstream ss;
  ss << s;
  string t;
  vector<string> ret;
  while (ss >> t) ret.push_back(t);
  return ret;
}
template <class K, class V>
vector<K> getKeys(map<K, V> m) {
  vector<K> keys;
  for (typeof((m).begin()) it = (m).begin(); it != (m).end(); ++it)
    keys.push_back(it->first);
  return keys;
}
inline double myRand() {
  return ((double)rand() / RAND_MAX) + ((double)rand() / RAND_MAX / RAND_MAX);
}
const double PI = 2.0 * acos(0.0);
struct Seg;
inline pair<double, double> operator|(pair<double, double> a, Seg s);
inline pair<double, double> operator||(pair<double, double> a, Seg s);
inline pair<double, double> operator-(pair<double, double> a,
                                      pair<double, double> b) {
  return pair<double, double>(a.first - b.first, a.second - b.second);
}
inline pair<double, double> operator+(pair<double, double> a,
                                      pair<double, double> b) {
  return pair<double, double>(a.first + b.first, a.second + b.second);
}
inline double operator*(pair<double, double> a, pair<double, double> b) {
  return a.first * b.first + a.second * b.second;
}
inline double operator^(pair<double, double> a, pair<double, double> b) {
  return a.first * b.second - a.second * b.first;
}
inline double operator!(pair<double, double> a) {
  return sqrt((double)(((a.first) * (a.first)) + ((a.second) * (a.second))));
}
inline pair<double, double> operator*(double first, pair<double, double> a) {
  return pair<double, double>(a.first * first, a.second * first);
}
inline pair<double, double> operator/(pair<double, double> a, double first) {
  return pair<double, double>(a.first / first, a.second / first);
}
inline pair<double, double> operator|(pair<double, double> a,
                                      pair<double, double> b) {
  return ((a * b) / (b * b)) * b;
}
inline pair<double, double> operator~(pair<double, double> a) { return a / !a; }
inline pair<double, double> operator&(pair<double, double> a) {
  return pair<double, double>(a.second, -a.first);
}
inline bool operator==(pair<double, double> a, pair<double, double> b) {
  return !(a - b) < EPS;
}
inline int ccw(pair<double, double> a, pair<double, double> b,
               pair<double, double> c) {
  return sign((b - a) ^ (c - a));
}
struct Seg {
  pair<double, double> a, b;
  Seg(pair<double, double> aa, pair<double, double> bb) : a(aa), b(bb) {}
  inline double operator!() { return !(a - b); }
  inline int onSeg(pair<double, double> p) {
    return !(a - b) + EPS > !(p - a) + !(p - b) && !(p - (p | (*this))) < EPS;
  }
  inline int onLine(pair<double, double> p) { return ccw(p, a, b) == 0; }
  inline double PLDist(pair<double, double> p) {
    return ((b - a) ^ (p - a)) / !(*this);
  }
  inline double PSDist(pair<double, double> p) {
    return onSeg(p | (*this)) ? PLDist(p) : min(!(p - a), !(p - b));
  }
  inline pair<double, double> *LLIntersect(Seg s) {
    pair<double, double> c = s.a, d = s.b;
    if (sign((b - a) ^ (d - c)) == 0) {
      return NULL;
    }
    double t = ((c - a) ^ (d - c)) / ((b - a) ^ (d - c));
    return new pair<double, double>(a + (t * (b - a)));
  }
  inline pair<double, double> *LSIntersect(Seg s) {
    return (ccw(s.a, a, b) * ccw(s.b, b, a) == 1) ? NULL : LLIntersect(s);
  }
  inline pair<double, double> *SSIntersect(Seg s) {
    pair<double, double> c = s.a, d = s.b;
    if (ccw(s.a, a, b) * ccw(s.b, b, a) == 1) return NULL;
    if (a == b) return s.onSeg(a) ? new pair<double, double>(a) : NULL;
    if (s.a == s.b) return onSeg(s.a) ? new pair<double, double>(s.a) : NULL;
    if (max(a.first, b.first) < min(c.first, d.first) - EPS) return NULL;
    if (min(a.first, b.first) > max(c.first, d.first) + EPS) return NULL;
    if (max(a.second, b.second) < min(c.second, d.second) - EPS) return NULL;
    if (min(a.second, b.second) > max(c.second, d.second) + EPS) return NULL;
    return LLIntersect(s);
  }
};
inline pair<double, double> operator|(pair<double, double> a, Seg s) {
  return a | (s.b - s.a);
}
inline pair<double, double> operator||(pair<double, double> a, Seg s) {
  pair<double, double> onLine = a | s;
  return onLine + (onLine - a);
}
struct Circle {
  pair<double, double> c;
  double r;
  Circle(pair<double, double> cc, double rr) : c(cc), r(rr) {}
  Circle(pair<double, double> a, pair<double, double> b,
         pair<double, double> c) {
    Seg bisAB((a + b) / 2, (a + b) / 2 + &(b - a));
    Seg bisBC((b + c) / 2, (b + c) / 2 + &(c - b));
    this->c = *(bisAB.LLIntersect(bisBC));
    r = !(a - this->c);
  }
  pair<pair<double, double>, pair<double, double> > *CCIntersect(Circle o) {
    double R = !(c - o.c);
    if (r + o.r < R - EPS || r + R < o.r - EPS || o.r + R < r - EPS)
      return NULL;
    double dsq = (c - o.c) * (c - o.c);
    pair<double, double> m =
        c + ((((r) * (r)) + dsq - ((o.r) * (o.r))) / (2 * dsq)) * (o.c - c);
    double h = sqrt(r * r - (m - c) * (m - c));
    pair<double, double> perp = &(~(o.c - c));
    return new pair<pair<double, double>, pair<double, double> >(
        make_pair(m + h * perp, m - h * perp));
  }
};
void myCode() {
  vector<pair<double, double> > pts;
  for (int i = (int)0; i < (int)3; ++i) {
    double first = getDouble(), second = getDouble();
    pts.push_back(pair<double, double>(first, second));
  }
  Circle circle(pts[0], pts[1], pts[2]);
  pair<double, double> t3 = circle.c;
  double r = circle.r;
  vector<double> thetas;
  for (int i = (int)0; i < (int)3; ++i)
    thetas.push_back(atan2(pts[i].second - t3.second, pts[i].first - t3.first));
  double a1 = thetas[0] - thetas[1] - 2 * PI;
  while (a1 < 0) a1 += 2 * PI;
  double a2 = thetas[1] - thetas[2] - 2 * PI;
  while (a2 < 0) a2 += 2 * PI;
  for (int i = 3; i <= 100; ++i) {
    double angle = 2 * PI / i;
    double t1 = a1;
    while (t1 + EPS > angle) t1 -= angle;
    double t2 = a2;
    while (t2 + EPS > angle) t2 -= angle;
    if (fabs(t1) < 2 * EPS && fabs(t2) < 2 * EPS) {
      pair<double, double> n1(r, 0);
      pair<double, double> n2(r * cos(angle), r * sin(angle));
      printf("%.8lf\n", (n1 ^ n2) / 2 * i);
      break;
    }
  }
}
int main() {
  srand(0);
  myCode();
  return 0;
}