#include <bits/stdc++.h>
int nextInt() {
  int x;
  scanf("%d", &x);
  return x;
}
double nextDouble() {
  double x;
  scanf("%lf", &x);
  return x;
}
long long nextLong() {
  long long x;
  scanf("%I64d", &x);
  return x;
}
char nextChar() {
  char x;
  scanf("%c", &x);
  return x;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long pow(long long a, long long b, long long MOD) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y);
      if (x > MOD) x %= MOD;
    }
    y = (y * y);
    if (y > MOD) y %= MOD;
    b /= 2;
  }
  return x;
}
int countBitSet(long long n) {
  int ans = 0;
  while (n != 0) {
    n -= (n & -n);
    ++ans;
  }
  return ans;
}
long long mod = 1e9 + 7;
const int N = 100100;
const int M = 10111;
const double EPS = (double)1e-6;
const double INF = 1e50;
using namespace std;
double fgcd(double x, double y) {
  if (y < EPS)
    return x;
  else
    return fgcd(y, fmod(x, y));
}
bool eq(double x, double y) { return abs(x - y) < EPS; }
bool isInt(double x) {
  int xx = (int)(x + EPS);
  return eq(x, xx);
}
struct Point {
 private:
  double x;
  double y;

 public:
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point(const Point &p) : x(p.x), y(p.y) {}
  void read() { scanf("%lf %lf", &x, &y); }
  double getX() { return this->x; }
  double getY() { return this->y; }
  Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
  Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
  Point operator*(double c) const { return Point(x * c, y * c); }
  Point operator/(double c) const { return Point(x / c, y / c); }
};
struct Line {
 private:
  Point a;
  Point b;
  double m;
  double c;

 public:
  Line() {}
  Line(Point a, Point b) : a(a), b(b) {
    if (this->hasDefinedSlope()) {
      this->m = (a.getY() - b.getY()) / (a.getX() - b.getX());
      this->c = -a.getX() * m + a.getY();
    } else {
      this->c = a.getX();
    }
  }
  double getLength() {
    return sqrt((a.getX() - b.getX()) * (a.getX() - b.getX()) +
                (a.getY() - b.getY()) * (a.getY() - b.getY()));
  }
  bool hasDefinedSlope() {
    return (this->m != INF) && !(abs(a.getX() - b.getX()) < EPS);
  }
  double getSolpe() { return this->m; }
  void setSlope(double m) { this->m = m; }
  double getDelta() { return this->c; }
  void setDelta(double c) { this->c = c; }
  void setOnePoint(Point p) { this->a = p; }
  bool isParallelToX() {
    return this->hasDefinedSlope() && this->getSolpe() == 0;
  }
  bool isParallelToY() { return !this->hasDefinedSlope(); }
  bool isParallelToLine(Line line) {
    if (this->isParallelToY() && line.isParallelToY()) return true;
    if (abs(this->getSolpe() - line.getSolpe()) < EPS) return true;
    return false;
  }
  Point getMidPoint() { return (this->a + this->b) / 2.0; }
  Line getPerpendicularBisector() {
    Point p = this->getMidPoint();
    Line line;
    line.setOnePoint(p);
    if (this->isParallelToX()) {
      line.setSlope(INF);
      line.setDelta(p.getX());
    } else if (this->isParallelToY()) {
      line.setSlope(0);
      line.setDelta(p.getY());
    } else {
      double mm = -1.0 / this->getSolpe();
      line.setSlope(mm);
      line.setDelta(-p.getX() * mm + p.getY());
    }
    return line;
  }
  Point getIntersectionPoint(Line line) {
    if (this->isParallelToLine(line)) return Point(INF, INF);
    if (this->isParallelToX()) {
      if (line.isParallelToY())
        return Point(line.getDelta(), this->getDelta());
      else
        return Point((this->getDelta() - line.getDelta()) / line.getSolpe(),
                     this->getDelta());
    } else if (this->isParallelToY()) {
      if (line.isParallelToX())
        return Point(this->getDelta(), line.getDelta());
      else
        Point(this->getDelta(),
              line.getSolpe() * this->getDelta() + line.getDelta());
    } else if (line.isParallelToX()) {
      return Point((line.getDelta() - this->getDelta()) / this->getSolpe(),
                   line.getDelta());
    } else if (line.isParallelToY()) {
      return Point(line.getDelta(),
                   this->getSolpe() * line.getDelta() + this->getDelta());
    }
    double x = (line.getDelta() - this->getDelta()) /
               (this->getSolpe() - line.getSolpe());
    double y = this->getSolpe() * x + this->getDelta();
    return Point(x, y);
  }
  double getDistanceToPoint(Point p) {
    if (this->isParallelToX()) return abs(p.getY() - this->a.getY());
    if (this->isParallelToY()) return abs(p.getX() - this->a.getX());
    double t1 = a.getY() - b.getY();
    double t2 = b.getX() - a.getX();
    double t3 = this->getDelta() * (a.getX() - b.getX());
    return (t1 * p.getX() + t2 * p.getY() + t3) / sqrt(t1 * t1 + t2 * t2);
  }
};
struct Vector {
 private:
  double x;
  double y;

 public:
  Vector() {}
  Vector(Point a, Point b) {
    x = b.getX() - a.getX();
    y = b.getY() - a.getY();
  }
  double dotProduct(Vector v) { return this->x * this->y + v.x * v.y; }
  double getLength() { return sqrt(this->x * this->x + this->y * this->y); }
  double getAngle(Vector v) {
    return acos(this->dotProduct(v) / (this->getLength() * v.getLength()));
  }
  double getX() { return x; }
  double getY() { return y; }
};
Point a[N];
int main() {
  int n = nextInt();
  for (int i = 0; i < n; i++) {
    a[i].read();
  }
  double ans = 1e50;
  for (int i = 0; i < n; i++) {
    int j = i > 0 ? i - 1 : n - 1;
    int k = j > 0 ? j - 1 : n - 1;
    Line line(a[k], a[i]);
    ans = min(ans, line.getDistanceToPoint(a[j]));
  }
  cout << fixed << setprecision(10) << ans / 2.0 << endl;
}

### Prompt

Please provide a Cpp coded solution 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>
int nextInt() {
  int x;
  scanf("%d", &x);
  return x;
}
double nextDouble() {
  double x;
  scanf("%lf", &x);
  return x;
}
long long nextLong() {
  long long x;
  scanf("%I64d", &x);
  return x;
}
char nextChar() {
  char x;
  scanf("%c", &x);
  return x;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long pow(long long a, long long b, long long MOD) {
  long long x = 1, y = a;
  while (b > 0) {
    if (b % 2 == 1) {
      x = (x * y);
      if (x > MOD) x %= MOD;
    }
    y = (y * y);
    if (y > MOD) y %= MOD;
    b /= 2;
  }
  return x;
}
int countBitSet(long long n) {
  int ans = 0;
  while (n != 0) {
    n -= (n & -n);
    ++ans;
  }
  return ans;
}
long long mod = 1e9 + 7;
const int N = 100100;
const int M = 10111;
const double EPS = (double)1e-6;
const double INF = 1e50;
using namespace std;
double fgcd(double x, double y) {
  if (y < EPS)
    return x;
  else
    return fgcd(y, fmod(x, y));
}
bool eq(double x, double y) { return abs(x - y) < EPS; }
bool isInt(double x) {
  int xx = (int)(x + EPS);
  return eq(x, xx);
}
struct Point {
 private:
  double x;
  double y;

 public:
  Point() {}
  Point(double x, double y) : x(x), y(y) {}
  Point(const Point &p) : x(p.x), y(p.y) {}
  void read() { scanf("%lf %lf", &x, &y); }
  double getX() { return this->x; }
  double getY() { return this->y; }
  Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
  Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
  Point operator*(double c) const { return Point(x * c, y * c); }
  Point operator/(double c) const { return Point(x / c, y / c); }
};
struct Line {
 private:
  Point a;
  Point b;
  double m;
  double c;

 public:
  Line() {}
  Line(Point a, Point b) : a(a), b(b) {
    if (this->hasDefinedSlope()) {
      this->m = (a.getY() - b.getY()) / (a.getX() - b.getX());
      this->c = -a.getX() * m + a.getY();
    } else {
      this->c = a.getX();
    }
  }
  double getLength() {
    return sqrt((a.getX() - b.getX()) * (a.getX() - b.getX()) +
                (a.getY() - b.getY()) * (a.getY() - b.getY()));
  }
  bool hasDefinedSlope() {
    return (this->m != INF) && !(abs(a.getX() - b.getX()) < EPS);
  }
  double getSolpe() { return this->m; }
  void setSlope(double m) { this->m = m; }
  double getDelta() { return this->c; }
  void setDelta(double c) { this->c = c; }
  void setOnePoint(Point p) { this->a = p; }
  bool isParallelToX() {
    return this->hasDefinedSlope() && this->getSolpe() == 0;
  }
  bool isParallelToY() { return !this->hasDefinedSlope(); }
  bool isParallelToLine(Line line) {
    if (this->isParallelToY() && line.isParallelToY()) return true;
    if (abs(this->getSolpe() - line.getSolpe()) < EPS) return true;
    return false;
  }
  Point getMidPoint() { return (this->a + this->b) / 2.0; }
  Line getPerpendicularBisector() {
    Point p = this->getMidPoint();
    Line line;
    line.setOnePoint(p);
    if (this->isParallelToX()) {
      line.setSlope(INF);
      line.setDelta(p.getX());
    } else if (this->isParallelToY()) {
      line.setSlope(0);
      line.setDelta(p.getY());
    } else {
      double mm = -1.0 / this->getSolpe();
      line.setSlope(mm);
      line.setDelta(-p.getX() * mm + p.getY());
    }
    return line;
  }
  Point getIntersectionPoint(Line line) {
    if (this->isParallelToLine(line)) return Point(INF, INF);
    if (this->isParallelToX()) {
      if (line.isParallelToY())
        return Point(line.getDelta(), this->getDelta());
      else
        return Point((this->getDelta() - line.getDelta()) / line.getSolpe(),
                     this->getDelta());
    } else if (this->isParallelToY()) {
      if (line.isParallelToX())
        return Point(this->getDelta(), line.getDelta());
      else
        Point(this->getDelta(),
              line.getSolpe() * this->getDelta() + line.getDelta());
    } else if (line.isParallelToX()) {
      return Point((line.getDelta() - this->getDelta()) / this->getSolpe(),
                   line.getDelta());
    } else if (line.isParallelToY()) {
      return Point(line.getDelta(),
                   this->getSolpe() * line.getDelta() + this->getDelta());
    }
    double x = (line.getDelta() - this->getDelta()) /
               (this->getSolpe() - line.getSolpe());
    double y = this->getSolpe() * x + this->getDelta();
    return Point(x, y);
  }
  double getDistanceToPoint(Point p) {
    if (this->isParallelToX()) return abs(p.getY() - this->a.getY());
    if (this->isParallelToY()) return abs(p.getX() - this->a.getX());
    double t1 = a.getY() - b.getY();
    double t2 = b.getX() - a.getX();
    double t3 = this->getDelta() * (a.getX() - b.getX());
    return (t1 * p.getX() + t2 * p.getY() + t3) / sqrt(t1 * t1 + t2 * t2);
  }
};
struct Vector {
 private:
  double x;
  double y;

 public:
  Vector() {}
  Vector(Point a, Point b) {
    x = b.getX() - a.getX();
    y = b.getY() - a.getY();
  }
  double dotProduct(Vector v) { return this->x * this->y + v.x * v.y; }
  double getLength() { return sqrt(this->x * this->x + this->y * this->y); }
  double getAngle(Vector v) {
    return acos(this->dotProduct(v) / (this->getLength() * v.getLength()));
  }
  double getX() { return x; }
  double getY() { return y; }
};
Point a[N];
int main() {
  int n = nextInt();
  for (int i = 0; i < n; i++) {
    a[i].read();
  }
  double ans = 1e50;
  for (int i = 0; i < n; i++) {
    int j = i > 0 ? i - 1 : n - 1;
    int k = j > 0 ? j - 1 : n - 1;
    Line line(a[k], a[i]);
    ans = min(ans, line.getDistanceToPoint(a[j]));
  }
  cout << fixed << setprecision(10) << ans / 2.0 << endl;
}

```