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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e3 + 8;
const double EPS = 1e-8;
inline int cmp(double x) {
  if (fabs(x) < EPS) return 0;
  if (x > 0) return 1;
  return -1;
}
const double pi = acos(-1.0);
inline double sqr(double x) { return x * x; }
struct point {
  double x, y;
  point() {}
  point(double a, double b) : x(a), y(b) {}
  void input() { cin >> x >> y; }
  friend point operator+(const point &a, const point &b) {
    return point(a.x + b.x, a.y + b.y);
  }
  friend point operator-(const point &a, const point &b) {
    return point(a.x - b.x, a.y - b.y);
  }
  friend bool operator==(const point &a, const point &b) {
    return (cmp(a.x - b.x) == 0) && (cmp(a.y - b.y) == 0);
  }
  friend point operator*(const point &a, const double &b) {
    return point(a.x * b, a.y * b);
  }
  friend point operator*(const double &a, const point &b) {
    return point(a * b.x, a * b.y);
  }
  friend point operator/(const point &a, const double &b) {
    return point(a.x / b, a.y / b);
  }
  double norm() { return sqrt(sqr(x) + sqr(y)); }
};
double det(const point &a, const point &b) { return a.x * b.y - a.y * b.x; }
double dot(const point &a, const point &b) { return a.x * b.x + a.y * b.y; }
double dist(const point &a, const point &b) { return (a - b).norm(); }
point rotate_point(const point &p, double A) {
  double tx = p.x, ty = p.y;
  return point(tx * cos(A) - ty * sin(A), tx * sin(A) + ty * cos(A));
}
struct line {
  point a, b;
  line() {}
  line(point x, point y) : a(x), b(y) {}
};
inline line point_make_line(const point &a, const point &b) {
  return line(a, b);
}
inline double dis_point_segment(const point &p, const point &s,
                                const point &t) {
  if (cmp(dot(p - s, t - s)) < 0) return (p - s).norm();
  if (cmp(dot(p - t, s - t)) < 0) return (p - t).norm();
  return fabs(det(s - p, t - p) / dist(s, t));
}
inline void PointProjLine(const point &p, const point &s, const point &t,
                          point &cp) {
  double r = dot((t - s), (p - s)) / dot(t - s, t - s);
  cp = s + r * (t - s);
}
inline bool PointOnSegment(const point &p, const point &s, const point &t) {
  return (cmp(det(p - s, t - s)) == 0) && (cmp(dot(p - s, p - t)) <= 0);
}
inline bool parallel(const line &a, const line &b) {
  return !cmp(det(a.a - a.b, b.a - b.b));
}
inline bool line_make_point(const line &a, const line &b, point &res) {
  if (parallel(a, b)) return false;
  double s1 = det(a.a - b.a, b.b - b.a);
  double s2 = det(a.b - b.a, b.b - b.a);
  res = (s1 * a.b - s2 * a.a) / (s1 - s2);
  return true;
}
inline line move_d(const line &a, const double &len) {
  point d = a.b - a.a;
  d = d / d.norm();
  d = rotate_point(d, pi / 2);
  return line(a.a + d * len, a.b + d * len);
}
point val[MAXN];
int n;
inline int mod(int x) { return x - x / n * n; }
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int i;
  double ans = 2e9 + 8;
  cin >> n;
  for (i = 0; i < n; i++) {
    val[i].input();
  }
  for (i = 0; i < n; i++) {
    ans = min(ans,
              dis_point_segment(val[mod(i + 1)], val[i], val[mod(i + 2)]) / 2);
  }
  cout << fixed << setprecision(10) << ans << endl;
  return 0;
}