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.
#include <bits/stdc++.h>
using namespace std;
inline int _Int() {
  int x;
  scanf("%d", &x);
  return x;
}
long long int bigMod(long long int A, long long int P, int M) {
  long long int R = 1;
  for (A %= M; P; P >>= 1) {
    if (P & 1) R = (R * A) % M;
    A = (A * A) % M;
  }
  return R;
}
long long int bigMul(long long int A, long long int B, long long int M) {
  long long int R = 0;
  for (A %= M; B; B >>= 1) {
    if (B & 1) R = (R + A) % M;
    A = (A + A) % M;
  }
  return R;
}
long long int negMod(long long int A, long long int B) {
  return (((A % B) + B) % B);
}
long long int invMod(long long int A, long long int M) {
  return bigMod(A, M - 2, M);
}
unsigned long long int _pow(unsigned long long int A, int P) {
  unsigned long long int R = 1;
  for (; P; P >>= 1) {
    if (P & 1) R = (R * A);
    A = (A * A);
  }
  return R;
}
template <class T>
T GCD(T x, T y) {
  while (x) x ^= y ^= x ^= y %= x;
  return y;
}
template <class T>
bool inRng(T u, T v, T x) {
  return u <= x && x <= v;
}
double EPS = 1e-7;
bool isEqual(double a, double b) { return (max(a, b) - min(a, b)) < EPS; }
bool inRange(double from, double key, double to) {
  return from <= key && key <= to;
}
struct Point {
  double x, y;
  Point() {}
  Point(double X, double Y) { x = X, y = 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); }
  bool operator<(const Point &R) const {
    return (x == R.x) ? (y < R.y) : (x < R.x);
  }
  double dist(Point &b) {
    return sqrt((x - b.x) * (x - b.x) + (y - b.y) * (y - b.y));
  }
  bool operator==(const Point &p) const {
    return isEqual(x, p.x) && isEqual(y, p.y);
  }
};
ostream &operator<<(ostream &os, const Point &p) {
  os << "( " << p.x << " , " << p.y << " )";
}
struct Vector {
  double x, y;
  Vector() {}
  Vector(Point a, Point b) { x = b.x - a.x, y = a.y - b.y; }
  Vector(double X, double Y) { x = X, y = Y; }
  Vector operator+(const Vector &Ref) const {
    return Vector(x + Ref.x, y + Ref.y);
  }
  Vector operator-(const Vector &Ref) const {
    return Vector(x - Ref.x, y - Ref.y);
  }
  bool operator==(const Vector &Ref) const {
    return isEqual(x, Ref.x) && isEqual(y, Ref.y);
  }
  Point endPoint(Point P) { return Point(x + P.x, P.y - y); }
  double magnitude() { return sqrt(x * x + y * y); }
  double dot(Vector &B) { return x * B.x + y * B.y; }
  double cross(Vector &B) { return x * B.y - y * B.x; }
  double angleClockwise(Vector &B) {
    double dot = this->x * B.x + this->y * B.y;
    double det = this->x * B.y - this->y * B.x;
    double angle = atan2(det, dot) * (180.0 / acos(-1));
    if (angle < 0) return 360.00 + angle;
    return angle;
  }
  Vector rotate(double theta) {
    Vector Ret;
    double ct = cos(theta * (acos(-1) / 180));
    double st = sin(theta * (acos(-1) / 180));
    Ret.x = x * ct - y * st;
    Ret.y = x * st + y * ct;
    return Ret;
  }
};
double linePointDist(Point a, Point b, Point p, bool isSegment) {
  Vector AB(a, b), BP(b, p), BA(b, a), AP(a, p);
  if (isSegment) {
    if (BA.cross(AP) > 0.00) return a.dist(p);
    if (AB.cross(BP) > 0.00) return b.dist(p);
  }
  return fabs(AB.cross(BP) / AB.magnitude());
}
int n;
Point P[1000 + 7];
void Main() {
  n = _Int();
  for (int i = 0; i < n; i++) {
    P[i].x = _Int();
    P[i].y = _Int();
  }
  double high = 1234687981321654L;
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      high = min(high, P[i].dist(P[j]) / 2.00);
    }
  }
  for (int i = 0; i < n; i++) {
    int j = (i + 1) % n, k = (i + 2) % n;
    double d = linePointDist(P[i], P[k], P[j], 0);
    high = min(high, d / 2.00);
  }
  printf("%0.8f\n", high);
  return;
}
int main() {
  Main();
  return 0;
}
