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;
void err(istream_iterator<string> it) {}
template <typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
  cerr << *it << " = " << a << "\n";
  err(++it, args...);
}
const double PI = acos(-1);
const double eps = (1e-9);
const long long int INF = 1e18;
const int M = (1e9) + 7;
const int N = 200000;
struct Point {
  int x, y;
  Point(int a = 0, int b = 0) { x = a, y = b; }
  void reassign(int a, int b) { x = a, y = b; }
  void input() { scanf("%d%d", &x, &y); }
  void print() { printf("%d %d\n", x, y); }
  Point operator+=(Point &A) {
    x += A.x, y += A.y;
    return *this;
  }
  Point operator-=(Point &A) {
    x -= A.x, y -= A.y;
    return *this;
  }
  Point operator+(Point &A) {
    Point tp(x + A.x, y + A.y);
    return tp;
  }
  Point operator-(Point &A) {
    Point tp(x - A.x, y - A.y);
    return tp;
  }
  Point operator*=(int f) {
    x *= f, y *= f;
    return *this;
  }
  Point operator/=(int f) {
    x /= f, y /= f;
    return *this;
  }
  bool operator==(Point &A) {
    if (x == A.x && y == A.y) return true;
    return false;
  }
  bool operator!=(Point &A) {
    if (x != A.x || y != A.y) return true;
    return false;
  }
  void ulta() { swap(x, y); }
};
Point makepoint(int a, int b) {
  Point temp(a, b);
  return temp;
}
void swap(Point &A, Point &B) {
  swap(A.x, B.x);
  swap(A.y, B.y);
}
bool cmp(Point &a, Point &b) {
  if (a.x != b.x) return (a.x < b.x);
  return (a.y < b.y);
}
long long int dotproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.x +
         (long long int)a.y * (long long int)b.y;
}
long long int crossproduct(Point a, Point b) {
  return (long long int)a.x * (long long int)b.y -
         (long long int)a.y * (long long int)b.x;
}
int ccw(Point a, Point b, Point origin = makepoint(0, 0)) {
  long long int x = crossproduct(a - origin, b - origin);
  if (x > 0) x = 1;
  if (x < 0) x = -1;
  return (int)x;
}
long long int sqrdis(Point a, Point b = makepoint(0, 0)) {
  long long int q = 0, temp;
  temp = a.x - b.x;
  temp *= temp, q += temp;
  temp = a.y - b.y;
  temp *= temp, q += temp;
  return q;
}
double dist(Point a, Point b = makepoint(0, 0)) {
  long long int temp = sqrdis(a, b);
  return sqrt(temp);
}
double norm(Point &a) {
  long long int temp = sqrdis(a);
  double d = sqrt(temp);
  return d;
}
double anglepolar(Point &a) { return atan2(a.y, a.x); }
double anglebetween(Point &a, Point &b, Point origin = makepoint(0, 0)) {
  return atan2(crossproduct(a - origin, b - origin),
               dotproduct(a - origin, b - origin));
}
Point perp(Point &a) { return makepoint(-a.y, a.x); }
pair<double, double> bisector(Point a, Point b) {
  double da, db;
  da = norm(a);
  db = norm(b);
  double p = 0, q = 0;
  p = da * b.x + db * a.x;
  q = da * b.y + db * a.y;
  return {p, q};
}
struct Line {
  Point a, b, ab;
  bool isline;
  Line() {
    a = makepoint(0, 0);
    b = a, ab = a, isline = 0;
  }
  Line(Point &p, Point &q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
  }
  void update(Point &p, Point &q) {
    a = p, b = q;
    ab = b - a;
    if (a != b)
      isline = 1;
    else
      isline = 0;
    return;
  }
  bool online(Point &point) {
    if (!isline) return (point == a);
    return (crossproduct(point - a, ab) == 0);
  }
  bool operator==(Line &other) {
    return ((crossproduct(ab, other.ab) == 0) && online(other.a));
  }
  bool onsegment(Point &point) {
    if (!isline) return (point == a);
    Point va, vb;
    va = a - point, vb = b - point;
    return (crossproduct(va, vb) == 0 && dotproduct(va, vb) <= 0);
  }
  bool parallel(Line &other) { return (crossproduct(ab, other.ab) == 0); }
  bool perpendicular(Line &other) { return (dotproduct(ab, other.ab) == 0); }
  double distline(Point &point) {
    if (!isline) return sqrt(sqrdis(a, point));
    long double t = abs(crossproduct(point - a, ab));
    t /= norm(ab);
    return t;
  }
  double distsegment(Point &point) {
    if (dotproduct(point - a, ab) <= 0) return dist(a, point);
    if (dotproduct(point - b, ab) >= 0) return dist(b, point);
    return distline(point);
  }
};
int main() {
  int i, n, a, b;
  scanf("%d", &n);
  vector<Point> v(n);
  for (i = 0; i < n; ++i) v[i].input();
  double d = INF;
  v.emplace_back(v[0]), v.emplace_back(v[1]);
  Line ray;
  cout << setprecision(10) << fixed;
  for (i = 1; i < n + 1; ++i) {
    ray.update(v[i - 1], v[i + 1]);
    d = min(d, ray.distline(v[i]));
  }
  d /= 2;
  cout << d << "\n";
}