#include <bits/stdc++.h>
const double EPS = 1e-6;
const double PI = 3.14159265359;
const double MAX_COORD = 1.1e9;
const double INF = 100 * MAX_COORD;
class Vector {
 private:
  static bool nearly_equal(double a, double b) {
    return (std::abs(a - b) < EPS);
  }

 public:
  double x, y;
  Vector(double pX = 0, double pY = 0) : x(pX), y(pY) {}
  double len_sqr() const { return x * x + y * y; }
  double len() const { return std::sqrt(len_sqr()); }
  Vector normal() const {
    double l = len();
    return Vector(x / l, y / l);
  }
  Vector &operator+=(const Vector &v) {
    x += v.x;
    y += v.y;
    return *this;
  }
  Vector &operator-=(const Vector &v) {
    x -= v.x;
    y -= v.y;
    return *this;
  }
  Vector &operator*=(double n) {
    x *= n;
    y *= n;
    return *this;
  }
  Vector operator-() { return Vector(-x, -y); }
  friend Vector operator+(Vector v, const Vector &u) { return v += u; }
  friend Vector operator-(Vector v, const Vector &u) { return v -= u; }
  friend Vector operator*(Vector v, double n) { return v *= n; }
  friend double operator*(Vector v, const Vector &u) {
    return v.x * u.x + v.y * u.y;
  }
  friend double operator^(Vector v, const Vector &u) {
    return v.x * u.y - v.y * u.x;
  }
  friend bool operator==(const Vector &v, const Vector &u) {
    return nearly_equal(v.x, u.x) && nearly_equal(v.y, u.y);
  }
  friend bool operator!=(const Vector &v, const Vector &u) { return !(v == u); }
};
struct Line {
  double x, y, c;
  Line(const Vector &v1 = Vector(), const Vector &v2 = Vector()) {
    x = v1.y - v2.y;
    y = v2.x - v1.x;
    c = v1.x * v2.y - v2.x * v1.y;
  }
  std::vector<Vector> intersect_circle(double r) {
    std::vector<Vector> ans;
    if (x != 0) {
      double d = y * y * c * c - (y * y + x * x) * (c * c - x * x * r * r);
      if (d < 0) {
        return ans;
      }
      double dSqrt = std::sqrt(d);
      Vector v1, v2;
      v1.y = (-y * c + dSqrt) / (x * x + y * y);
      v2.y = (-y * c - dSqrt) / (x * x + y * y);
      v1.x = (-c - y * v1.y) / x;
      v2.x = (-c - y * v2.y) / x;
      ans.push_back(v1);
      if (v1 != v2) {
        ans.push_back(v2);
      }
    } else {
      double d = x * x * c * c - (x * x + y * y) * (c * c - y * y * r * r);
      if (d < 0) {
        return ans;
      }
      double dSqrt = std::sqrt(d);
      Vector v1, v2;
      v1.x = (-x * c + dSqrt) / (x * x + y * y);
      v2.x = (-x * c - dSqrt) / (x * x + y * y);
      v1.y = (-c - x * v1.x) / y;
      v2.y = (-c - x * v2.x) / y;
      ans.push_back(v1);
      if (v1 != v2) {
        ans.push_back(v2);
      }
    }
    return ans;
  }
};
struct LineSegment {
 private:
  bool between(double v, double e1, double e2) {
    if (e1 < e2) {
      return ((v + EPS > e1) && (v < e2 + EPS));
    } else {
      return ((v + EPS > e2) && (v < e1 + EPS));
    }
  }

 public:
  Vector a, b;
  Line l;
  LineSegment(Vector pA = Vector(), Vector pB = Vector()) : a(pA), b(pB) {
    l = Line(a, b);
  }
  std::vector<Vector> intersect_circle(double r) {
    std::vector<Vector> pot = l.intersect_circle(r);
    std::vector<Vector> ans;
    for (const Vector &v : pot) {
      if (between(v.x, a.x, b.x) && between(v.y, a.y, b.y)) {
        ans.push_back(v);
      }
    }
    if (ans.size() == 2) {
      if (between(ans[0].x, ans[1].x, b.x) &&
          between(ans[0].y, ans[1].y, b.y)) {
        std::swap(ans[0], ans[1]);
      }
    }
    return ans;
  }
};
std::vector<Vector> poly;
uint32_t maxD;
void input() {
  uint32_t vCnt;
  scanf("%u", &vCnt);
  poly.resize(vCnt);
  for (uint32_t i = 0; i < vCnt; i++) {
    scanf("%lf %lf", &poly[i].x, &poly[i].y);
  }
}
double possib(Vector a, Vector b, Vector c) {
  double area = std::abs((b - a) ^ (c - b));
  double height = area / (a - c).len();
  return height / 2;
}
int main() {
  input();
  double num = INF;
  for (uint32_t i = 0; i < poly.size(); i++) {
    double c = possib(poly[i], poly[(i + 1) % poly.size()],
                      poly[(i + 2) % poly.size()]);
    num = std::min(num, c);
  }
  printf("%.7lf\n", num);
}

### Prompt

Please formulate a cpp solution to the following problem:

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>
const double EPS = 1e-6;
const double PI = 3.14159265359;
const double MAX_COORD = 1.1e9;
const double INF = 100 * MAX_COORD;
class Vector {
 private:
  static bool nearly_equal(double a, double b) {
    return (std::abs(a - b) < EPS);
  }

 public:
  double x, y;
  Vector(double pX = 0, double pY = 0) : x(pX), y(pY) {}
  double len_sqr() const { return x * x + y * y; }
  double len() const { return std::sqrt(len_sqr()); }
  Vector normal() const {
    double l = len();
    return Vector(x / l, y / l);
  }
  Vector &operator+=(const Vector &v) {
    x += v.x;
    y += v.y;
    return *this;
  }
  Vector &operator-=(const Vector &v) {
    x -= v.x;
    y -= v.y;
    return *this;
  }
  Vector &operator*=(double n) {
    x *= n;
    y *= n;
    return *this;
  }
  Vector operator-() { return Vector(-x, -y); }
  friend Vector operator+(Vector v, const Vector &u) { return v += u; }
  friend Vector operator-(Vector v, const Vector &u) { return v -= u; }
  friend Vector operator*(Vector v, double n) { return v *= n; }
  friend double operator*(Vector v, const Vector &u) {
    return v.x * u.x + v.y * u.y;
  }
  friend double operator^(Vector v, const Vector &u) {
    return v.x * u.y - v.y * u.x;
  }
  friend bool operator==(const Vector &v, const Vector &u) {
    return nearly_equal(v.x, u.x) && nearly_equal(v.y, u.y);
  }
  friend bool operator!=(const Vector &v, const Vector &u) { return !(v == u); }
};
struct Line {
  double x, y, c;
  Line(const Vector &v1 = Vector(), const Vector &v2 = Vector()) {
    x = v1.y - v2.y;
    y = v2.x - v1.x;
    c = v1.x * v2.y - v2.x * v1.y;
  }
  std::vector<Vector> intersect_circle(double r) {
    std::vector<Vector> ans;
    if (x != 0) {
      double d = y * y * c * c - (y * y + x * x) * (c * c - x * x * r * r);
      if (d < 0) {
        return ans;
      }
      double dSqrt = std::sqrt(d);
      Vector v1, v2;
      v1.y = (-y * c + dSqrt) / (x * x + y * y);
      v2.y = (-y * c - dSqrt) / (x * x + y * y);
      v1.x = (-c - y * v1.y) / x;
      v2.x = (-c - y * v2.y) / x;
      ans.push_back(v1);
      if (v1 != v2) {
        ans.push_back(v2);
      }
    } else {
      double d = x * x * c * c - (x * x + y * y) * (c * c - y * y * r * r);
      if (d < 0) {
        return ans;
      }
      double dSqrt = std::sqrt(d);
      Vector v1, v2;
      v1.x = (-x * c + dSqrt) / (x * x + y * y);
      v2.x = (-x * c - dSqrt) / (x * x + y * y);
      v1.y = (-c - x * v1.x) / y;
      v2.y = (-c - x * v2.x) / y;
      ans.push_back(v1);
      if (v1 != v2) {
        ans.push_back(v2);
      }
    }
    return ans;
  }
};
struct LineSegment {
 private:
  bool between(double v, double e1, double e2) {
    if (e1 < e2) {
      return ((v + EPS > e1) && (v < e2 + EPS));
    } else {
      return ((v + EPS > e2) && (v < e1 + EPS));
    }
  }

 public:
  Vector a, b;
  Line l;
  LineSegment(Vector pA = Vector(), Vector pB = Vector()) : a(pA), b(pB) {
    l = Line(a, b);
  }
  std::vector<Vector> intersect_circle(double r) {
    std::vector<Vector> pot = l.intersect_circle(r);
    std::vector<Vector> ans;
    for (const Vector &v : pot) {
      if (between(v.x, a.x, b.x) && between(v.y, a.y, b.y)) {
        ans.push_back(v);
      }
    }
    if (ans.size() == 2) {
      if (between(ans[0].x, ans[1].x, b.x) &&
          between(ans[0].y, ans[1].y, b.y)) {
        std::swap(ans[0], ans[1]);
      }
    }
    return ans;
  }
};
std::vector<Vector> poly;
uint32_t maxD;
void input() {
  uint32_t vCnt;
  scanf("%u", &vCnt);
  poly.resize(vCnt);
  for (uint32_t i = 0; i < vCnt; i++) {
    scanf("%lf %lf", &poly[i].x, &poly[i].y);
  }
}
double possib(Vector a, Vector b, Vector c) {
  double area = std::abs((b - a) ^ (c - b));
  double height = area / (a - c).len();
  return height / 2;
}
int main() {
  input();
  double num = INF;
  for (uint32_t i = 0; i < poly.size(); i++) {
    double c = possib(poly[i], poly[(i + 1) % poly.size()],
                      poly[(i + 2) % poly.size()]);
    num = std::min(num, c);
  }
  printf("%.7lf\n", num);
}

```