#include <bits/stdc++.h>
template <class T>
struct Polygon;
template <class T, unsigned N>
struct LineSegment;
enum Orientation { CW, CCW, CL };
template <class T, unsigned N>
struct Point;
template <class T>
struct sort_around_point;
template <class T, unsigned N>
struct Point {
  std::array<T, N> xs;
  Point() = default;
  explicit Point(const std::array<T, N> &xs) : xs(xs) {}
  explicit Point(std::istream &stream) {
    for (unsigned i = 0; i < N; i++) {
      stream >> xs[i];
    }
  };
  const T &operator[](unsigned i) const { return xs[i]; }
  T &operator[](unsigned i) { return xs[i]; }
  bool operator==(const Point<T, N> &rhs) const {
    for (unsigned i = 0; i < N; i++) {
      if (xs[i] != rhs[i]) {
        return false;
      }
    }
    return true;
  }
  bool operator<(const Point<T, N> &rhs) const {
    for (unsigned i = 0; i < N; i++) {
      if (xs[i] != rhs[i]) {
        return xs[i] < rhs[i];
      }
    }
    return false;
  }
  Point<T, N> operator+(const Point<T, N> &rhs) const {
    Point<T, N> p;
    for (unsigned i = 0; i < N; i++) {
      p[i] = xs[i] + rhs[i];
    }
    return p;
  }
  Point<T, N> operator-(const Point<T, N> &rhs) const {
    Point<T, N> p;
    for (unsigned i = 0; i < N; i++) {
      p.xs[i] = xs[i] - rhs[i];
    }
    return p;
  }
  std::string serialize() const {
    std::string s = "";
    for (const T &x : xs) {
      s += std::to_string(x) + " ";
    }
    s.pop_back();
    return s;
  }
};
template <class T>
struct sort_around_point {
  Point<T, 2> orig;
  explicit sort_around_point(const Point<T, 2> &orig) : orig(orig) {}
  inline bool operator()(const Point<T, 2> &lhs, const Point<T, 2> &rhs) {
    Point<T, 2> dl = lhs - orig, dr = rhs - orig;
    return atan2(dl[1], dl[0]) < atan2(dr[1], dr[0]);
  }
};
template <class T, unsigned N>
struct LineSegment {
  Point<T, N> p, q;
  LineSegment(const Point<T, N> &p, const Point<T, N> &q) : p(p), q(q) {}
  bool overlap(const LineSegment<T, 2> &rhs) const {
    return Polygon<T>({p, q, rhs.p}).orientation() == Orientation::CL &&
           (overlap_util(rhs.p) || overlap_util(rhs.q));
  }
  bool intersect(const LineSegment<T, 2> &rhs) const {
    Orientation a = Polygon<T>({p, q, rhs.p}).orientation(),
                b = Polygon<T>({p, q, rhs.q}).orientation(),
                c = Polygon<T>({rhs.p, rhs.q, p}).orientation(),
                d = Polygon<T>({rhs.p, rhs.q, q}).orientation();
    return (a != b && c != d) || overlap(rhs) || rhs.overlap(*this);
  }
  T sq_length() const {
    T s = 0;
    for (unsigned i = 0; i < N; i++) {
      s += (p[i] - q[i]) * (p[i] - q[i]);
    }
    return s;
  }
  T length() const { return std::sqrt(sq_length()); }
  Point<T, N> midpoint() const {
    Point<T, N> m;
    for (unsigned i = 0; i < N; i++) {
      m[i] = (p[i] + q[i]) / 2;
    }
    return m;
  }
  LineSegment<T, N> double_segment() const {
    return LineSegment<T, N>(p, q + (q - p));
  }

 private:
  bool overlap_util(const Point<T, N> &r) const {
    for (unsigned i = 0; i < N; i++) {
      if (r[i] < std::min(p[i], q[i]) || r[i] > std::max(p[i], q[i])) {
        return false;
      }
    }
    return true;
  }
};
template <class T>
struct LineSegmentSet;
template <class T>
struct LineSegmentSet {
  struct Event {};
  std::vector<LineSegment<T, 2>> ps;
  std::vector<Event> es;
  LineSegmentSet() = default;
  explicit LineSegmentSet(const std::vector<LineSegment<T, 2>> &ps) : ps(ps) {}
  const Point<T, 2> &operator[](unsigned i) const { return ps[i]; }
  Point<T, 2> &operator[](unsigned i) { return ps[i]; }
  std::vector<std::pair<unsigned, unsigned>> intersecting() const {
    std::priority_queue<Point<T, 2>> pq;
    return {};
  }
};
template <class T>
struct Polygon {
  std::vector<Point<T, 2>> ps;
  Polygon() = default;
  explicit Polygon(const std::vector<Point<T, 2>> &ps) : ps(ps) {}
  explicit Polygon(std::istream &stream, unsigned length) {
    for (unsigned i = 0; i < length; i++) {
      ps.push_back(Point<T, 2>(stream));
    }
  }
  const Point<T, 2> &operator[](unsigned i) const { return ps[i]; }
  Point<T, 2> &operator[](unsigned i) { return ps[i]; }
  std::string serialize() const {
    std::string s = std::to_string(ps.size()) + "\n";
    for (const Point<T, 2> p : ps) {
      s += p.serialize() + "\n";
    }
    return s;
  }
  T signed_double_area() const {
    T total = 0;
    for (unsigned i = 0; i < ps.size(); i++) {
      total += ps[i][0] * ps[succ(i)][1] - ps[succ(i)][0] * ps[i][1];
    }
    return total;
  }
  T double_area() const { return std::abs(signed_double_area()); }
  T area() const { return double_area() / 2; }
  LineSegmentSet<T> line_segments() const {
    std::vector<LineSegment<T, 2>> segments;
    for (unsigned i = 0; i < ps.size(); i++) {
      segments.push_back(LineSegment<T, 2>(ps[i], ps[succ(i)]));
    }
    return LineSegmentSet<T>(segments);
  }
  bool simple() const {
    return line_segments().intersecting().size() == ps.size();
  }
  Polygon<T> convex_hull(const bool strict) const {
    std::vector<Point<T, 2>> sorted(ps), hull(2 * ps.size());
    sort(sorted.begin(), sorted.end());
    sorted.erase(std::unique(sorted.begin(), sorted.end()), sorted.end());
    int n = sorted.size(), k = 0;
    if (n == 1) {
      return Polygon<T>(sorted);
    }
    for (int i = 0; i < n; i++) {
      Orientation o;
      do {
        o = Polygon<T>({hull[k - 2], hull[k - 1], sorted[i]}).orientation();
      } while (k-- >= 2 && (o != CW || (!strict && o == CL)));
      hull[k++] = sorted[i];
    }
    for (int i = n - 2, t = k + 1; i >= 0; i--) {
      Orientation o;
      do {
        o = Polygon<T>({hull[k - 2], hull[k - 1], sorted[i]}).orientation();
      } while (k-- >= t && (o != CW || (!strict && o == CL)));
      hull[k++] = sorted[i];
    }
    hull.resize(k - 1);
    reverse(hull.begin(), hull.end());
    return Polygon<T>(hull);
  }
  Orientation orientation() const {
    T v = signed_double_area();
    return v == 0 ? Orientation::CL
                  : (v < 0 ? Orientation::CW : Orientation::CCW);
  }
  std::vector<Point<T, 2>> right_angles() const {
    std::vector<Point<T, 2>> right;
    for (unsigned i = 0; i < ps.size(); i++) {
      LineSegment<T, 2> a(ps[pred(i)], ps[i]), b(ps[i], ps[succ(i)]),
          c(ps[pred(i)], ps[succ(i)]);
      if (a.sq_length() + b.sq_length() == c.sq_length()) {
        right.push_back(ps[i]);
      }
    }
    return right;
  }
  unsigned pred(unsigned i) const { return (i + ps.size() - 1) % ps.size(); }
  unsigned succ(unsigned i) const { return (i + 1) % ps.size(); }
};
using std::cin;
using std::cout;
using std::endl;
using std::min;
using std::setprecision;
using std::sqrt;
using std::string;
using std::vector;
int main() {
  int n;
  cin >> n;
  Polygon<double> p(cin, n);
  double ans = 1 << 30;
  for (int j = 0; j < n; j++) {
    int i = p.pred(j), k = p.succ(j);
    Polygon<double> tgl({p[i], p[j], p[k]});
    LineSegment<double, 2> base({p[i], p[k]});
    double h = 2 * tgl.area() / base.length();
    ans = min(ans, h / 2.0);
  }
  cout << setprecision(20) << ans << endl;
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

Input

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

Output

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

4
0 0
0 1
1 1
1 0


Output

0.3535533906


Input

6
5 0
10 0
12 -4
10 -8
5 -8
3 -4


Output

1.0000000000

Note

Here is a picture of the first sample

<image>

Here is an example of making the polygon non-convex.

<image>

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

### Response

```cpp
#include <bits/stdc++.h>
template <class T>
struct Polygon;
template <class T, unsigned N>
struct LineSegment;
enum Orientation { CW, CCW, CL };
template <class T, unsigned N>
struct Point;
template <class T>
struct sort_around_point;
template <class T, unsigned N>
struct Point {
  std::array<T, N> xs;
  Point() = default;
  explicit Point(const std::array<T, N> &xs) : xs(xs) {}
  explicit Point(std::istream &stream) {
    for (unsigned i = 0; i < N; i++) {
      stream >> xs[i];
    }
  };
  const T &operator[](unsigned i) const { return xs[i]; }
  T &operator[](unsigned i) { return xs[i]; }
  bool operator==(const Point<T, N> &rhs) const {
    for (unsigned i = 0; i < N; i++) {
      if (xs[i] != rhs[i]) {
        return false;
      }
    }
    return true;
  }
  bool operator<(const Point<T, N> &rhs) const {
    for (unsigned i = 0; i < N; i++) {
      if (xs[i] != rhs[i]) {
        return xs[i] < rhs[i];
      }
    }
    return false;
  }
  Point<T, N> operator+(const Point<T, N> &rhs) const {
    Point<T, N> p;
    for (unsigned i = 0; i < N; i++) {
      p[i] = xs[i] + rhs[i];
    }
    return p;
  }
  Point<T, N> operator-(const Point<T, N> &rhs) const {
    Point<T, N> p;
    for (unsigned i = 0; i < N; i++) {
      p.xs[i] = xs[i] - rhs[i];
    }
    return p;
  }
  std::string serialize() const {
    std::string s = "";
    for (const T &x : xs) {
      s += std::to_string(x) + " ";
    }
    s.pop_back();
    return s;
  }
};
template <class T>
struct sort_around_point {
  Point<T, 2> orig;
  explicit sort_around_point(const Point<T, 2> &orig) : orig(orig) {}
  inline bool operator()(const Point<T, 2> &lhs, const Point<T, 2> &rhs) {
    Point<T, 2> dl = lhs - orig, dr = rhs - orig;
    return atan2(dl[1], dl[0]) < atan2(dr[1], dr[0]);
  }
};
template <class T, unsigned N>
struct LineSegment {
  Point<T, N> p, q;
  LineSegment(const Point<T, N> &p, const Point<T, N> &q) : p(p), q(q) {}
  bool overlap(const LineSegment<T, 2> &rhs) const {
    return Polygon<T>({p, q, rhs.p}).orientation() == Orientation::CL &&
           (overlap_util(rhs.p) || overlap_util(rhs.q));
  }
  bool intersect(const LineSegment<T, 2> &rhs) const {
    Orientation a = Polygon<T>({p, q, rhs.p}).orientation(),
                b = Polygon<T>({p, q, rhs.q}).orientation(),
                c = Polygon<T>({rhs.p, rhs.q, p}).orientation(),
                d = Polygon<T>({rhs.p, rhs.q, q}).orientation();
    return (a != b && c != d) || overlap(rhs) || rhs.overlap(*this);
  }
  T sq_length() const {
    T s = 0;
    for (unsigned i = 0; i < N; i++) {
      s += (p[i] - q[i]) * (p[i] - q[i]);
    }
    return s;
  }
  T length() const { return std::sqrt(sq_length()); }
  Point<T, N> midpoint() const {
    Point<T, N> m;
    for (unsigned i = 0; i < N; i++) {
      m[i] = (p[i] + q[i]) / 2;
    }
    return m;
  }
  LineSegment<T, N> double_segment() const {
    return LineSegment<T, N>(p, q + (q - p));
  }

 private:
  bool overlap_util(const Point<T, N> &r) const {
    for (unsigned i = 0; i < N; i++) {
      if (r[i] < std::min(p[i], q[i]) || r[i] > std::max(p[i], q[i])) {
        return false;
      }
    }
    return true;
  }
};
template <class T>
struct LineSegmentSet;
template <class T>
struct LineSegmentSet {
  struct Event {};
  std::vector<LineSegment<T, 2>> ps;
  std::vector<Event> es;
  LineSegmentSet() = default;
  explicit LineSegmentSet(const std::vector<LineSegment<T, 2>> &ps) : ps(ps) {}
  const Point<T, 2> &operator[](unsigned i) const { return ps[i]; }
  Point<T, 2> &operator[](unsigned i) { return ps[i]; }
  std::vector<std::pair<unsigned, unsigned>> intersecting() const {
    std::priority_queue<Point<T, 2>> pq;
    return {};
  }
};
template <class T>
struct Polygon {
  std::vector<Point<T, 2>> ps;
  Polygon() = default;
  explicit Polygon(const std::vector<Point<T, 2>> &ps) : ps(ps) {}
  explicit Polygon(std::istream &stream, unsigned length) {
    for (unsigned i = 0; i < length; i++) {
      ps.push_back(Point<T, 2>(stream));
    }
  }
  const Point<T, 2> &operator[](unsigned i) const { return ps[i]; }
  Point<T, 2> &operator[](unsigned i) { return ps[i]; }
  std::string serialize() const {
    std::string s = std::to_string(ps.size()) + "\n";
    for (const Point<T, 2> p : ps) {
      s += p.serialize() + "\n";
    }
    return s;
  }
  T signed_double_area() const {
    T total = 0;
    for (unsigned i = 0; i < ps.size(); i++) {
      total += ps[i][0] * ps[succ(i)][1] - ps[succ(i)][0] * ps[i][1];
    }
    return total;
  }
  T double_area() const { return std::abs(signed_double_area()); }
  T area() const { return double_area() / 2; }
  LineSegmentSet<T> line_segments() const {
    std::vector<LineSegment<T, 2>> segments;
    for (unsigned i = 0; i < ps.size(); i++) {
      segments.push_back(LineSegment<T, 2>(ps[i], ps[succ(i)]));
    }
    return LineSegmentSet<T>(segments);
  }
  bool simple() const {
    return line_segments().intersecting().size() == ps.size();
  }
  Polygon<T> convex_hull(const bool strict) const {
    std::vector<Point<T, 2>> sorted(ps), hull(2 * ps.size());
    sort(sorted.begin(), sorted.end());
    sorted.erase(std::unique(sorted.begin(), sorted.end()), sorted.end());
    int n = sorted.size(), k = 0;
    if (n == 1) {
      return Polygon<T>(sorted);
    }
    for (int i = 0; i < n; i++) {
      Orientation o;
      do {
        o = Polygon<T>({hull[k - 2], hull[k - 1], sorted[i]}).orientation();
      } while (k-- >= 2 && (o != CW || (!strict && o == CL)));
      hull[k++] = sorted[i];
    }
    for (int i = n - 2, t = k + 1; i >= 0; i--) {
      Orientation o;
      do {
        o = Polygon<T>({hull[k - 2], hull[k - 1], sorted[i]}).orientation();
      } while (k-- >= t && (o != CW || (!strict && o == CL)));
      hull[k++] = sorted[i];
    }
    hull.resize(k - 1);
    reverse(hull.begin(), hull.end());
    return Polygon<T>(hull);
  }
  Orientation orientation() const {
    T v = signed_double_area();
    return v == 0 ? Orientation::CL
                  : (v < 0 ? Orientation::CW : Orientation::CCW);
  }
  std::vector<Point<T, 2>> right_angles() const {
    std::vector<Point<T, 2>> right;
    for (unsigned i = 0; i < ps.size(); i++) {
      LineSegment<T, 2> a(ps[pred(i)], ps[i]), b(ps[i], ps[succ(i)]),
          c(ps[pred(i)], ps[succ(i)]);
      if (a.sq_length() + b.sq_length() == c.sq_length()) {
        right.push_back(ps[i]);
      }
    }
    return right;
  }
  unsigned pred(unsigned i) const { return (i + ps.size() - 1) % ps.size(); }
  unsigned succ(unsigned i) const { return (i + 1) % ps.size(); }
};
using std::cin;
using std::cout;
using std::endl;
using std::min;
using std::setprecision;
using std::sqrt;
using std::string;
using std::vector;
int main() {
  int n;
  cin >> n;
  Polygon<double> p(cin, n);
  double ans = 1 << 30;
  for (int j = 0; j < n; j++) {
    int i = p.pred(j), k = p.succ(j);
    Polygon<double> tgl({p[i], p[j], p[k]});
    LineSegment<double, 2> base({p[i], p[k]});
    double h = 2 * tgl.area() / base.length();
    ans = min(ans, h / 2.0);
  }
  cout << setprecision(20) << ans << endl;
  return 0;
}

```