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;
struct point {
  double x, y;
  point() { x = y = 0.0; }
  point(double _x, double _y) : x(_x), y(_y) {}
  bool operator<(point other) const {
    if (fabs(x - other.x) > 1e-9) return x < other.x;
    return y < other.y;
  }
  bool operator>(point other) const {
    if (fabs(x - other.x) > 1e-9) return x > other.x;
    return y > other.y;
  }
  bool operator==(point other) const {
    return (fabs(x - other.x) < 1e-9 && (fabs(y - other.y) < 1e-9));
  }
};
double DEG_to_RAD(double t) { return t * M_PI / 180.0; }
double RAD_to_DEG(double t) { return t * 180.0 / M_PI; }
point rotate(point p, double theta) {
  double rad = DEG_to_RAD(theta);
  point t;
  if (fabs(p.x * cos(rad) - p.y * sin(rad)) < 1e-9)
    t.x = 0.0;
  else
    t.x = p.x * cos(rad) - p.y * sin(rad);
  if (fabs(p.x * sin(rad) + p.y * cos(rad)) < 1e-9)
    t.y = 0.0;
  else
    t.y = p.x * sin(rad) + p.y * cos(rad);
  return t;
}
double dist(point p1, point p2) { return hypot(p1.x - p2.x, p1.y - p2.y); }
struct line {
  double a, b, c;
};
void pointsToLine(point p1, point p2, line &l) {
  if (fabs(p1.x - p2.x) < 1e-9) {
    l.a = 1.0;
    l.b = 0.0;
    l.c = -p1.x;
  } else {
    l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x);
    l.b = 1.0;
    l.c = -(double)(l.a * p1.x) - p1.y;
  }
}
void point_and_m_ToLine(point p, double m, line &l) {
  l.a = -1 * m;
  l.b = 1;
  l.c = m * p.x - p.y;
}
bool areParallel(line l1, line l2) {
  return (fabs(l1.a - l2.a) < 1e-9) && (fabs(l1.b - l2.b) < 1e-9);
}
bool areSame(line l1, line l2) {
  return areParallel(l1, l2) && (fabs(l1.c - l2.c) < 1e-9);
}
bool areIntersect(line l1, line l2, point &p) {
  if (areParallel(l1, l2)) return false;
  p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);
  if (fabs(l1.b) > 1e-9)
    p.y = -(l1.a * p.x + l1.c);
  else
    p.y = -(l2.a * p.x + l2.c);
  return true;
}
struct vec {
  double x, y;
  vec(double _x, double _y) : x(_x), y(_y) {}
};
vec toVec(point a, point b) { return vec(b.x - a.x, b.y - a.y); }
vec scale(vec v, double s) { return vec(v.x * s, v.y * s); }
point translate(point p, vec v) {
  point t;
  if (fabs(p.x + v.x) < 1e-9)
    t.x = 0.0;
  else
    t.x = p.x + v.x;
  if (fabs(p.y + v.y) < 1e-9)
    t.y = 0.0;
  else
    t.y = p.y + v.y;
  return t;
}
double dot(vec a, vec b) { return (a.x * b.x + a.y * b.y); }
double norm_sq(vec v) { return v.x * v.x + v.y * v.y; }
double distToLine(point p, point a, point b, point &c) {
  vec ap = toVec(a, p), ab = toVec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  c = translate(a, scale(ab, u));
  return dist(p, c);
}
double distToLineSegment(point p, point a, point b, point &c) {
  vec ap = toVec(a, p), ab = toVec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  if (u < 0.0) {
    c = point(a.x, a.y);
    return dist(p, a);
  }
  if (u > 1.0) {
    c = point(b.x, b.y);
    return dist(p, b);
  }
  return distToLine(p, a, b, c);
}
double angle(point a, point o, point b) {
  vec oa = toVec(o, a), ob = toVec(o, b);
  return acos(dot(oa, ob) / sqrt(norm_sq(oa) * norm_sq(ob)));
}
long long Pow(long long b, long long p) {
  if (p == 0) return 1;
  if (p == 1) return b;
  if (p % 2 == 1) return b * Pow(b, p - 1);
  long long r = Pow(b, p / 2);
  return r * r;
}
double Triangle_area(double a, double b, double c) {
  double v = 0.5 * (a + b + c);
  return sqrt(v * (v - a) * (v - b) * (v - c));
}
long double teta(long double a, long double b, long double c) {
  long double s = Triangle_area(a, b, c);
  if (c > (sqrt(Pow(a, 2) + Pow(b, 2))))
    return M_PI - (asin((2 * s) / (a * b)));
  else
    return (asin((2 * s) / (a * b)));
}
double get_height(point a, point b, point c) {
  double tet = angle(b, a, c);
  return sin(tet) * dist(a, b);
}
int main() {
  point a[100005];
  int n;
  double m = 1e15;
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i].x >> a[i].y;
  for (int i = 0; i < n; i++) {
    point p1 = a[i];
    point p2 = a[(i + 1) % n];
    point p3 = a[(i + 2) % n];
    point p4;
    double t = distToLineSegment(p2, p1, p3, p4);
    t /= 2;
    m = min(m, t);
  }
  cout << fixed << setprecision(10) << m;
  return 0;
}