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 MOD = 1e9 + 7;
const int N = 100011;
struct point_i {
  int x, y;
  point_i() { x = y = 0; }
  point_i(int _x, int _y) : x(_x), y(_y) {}
};
struct pp {
  double x, y;
  pp() { x = y = 0.0; }
  pp(double _x, double _y) : x(_x), y(_y) {}
};
struct line {
  double a, b, c;
};
struct vec {
  double x, y;
  vec(double _x, double _y) : x(_x), y(_y) {}
};
double hypot(double x, int y) { return sqrt(x * x + y * y); }
double dist(pp p1, pp p2) { return hypot(p1.x - p2.x, p1.y - p2.y); }
double DEG_to_RAD(double theta) {
  return theta * (180.0 / 3.14159265358979323846);
}
void pointsToLine(pp p1, pp 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;
  }
}
vec toVec(pp a, pp 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); }
pp translate(pp p, vec v) { return pp(p.x + v.x, p.y + v.y); }
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(pp p, pp a, pp b, pp &c) {
  vec ap = toVec(a, p);
  vec ab = toVec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  c = translate(a, scale(ab, u));
  return dist(p, c);
}
double distToLineSegment(pp p, pp a, pp b, pp &c) {
  vec ap = toVec(a, p);
  vec ab = toVec(a, b);
  double u = dot(ap, ab) / norm_sq(ab);
  if (u < 0.0) {
    c = pp(a.x, a.y);
    return dist(p, a);
  } else if (u > 1.0) {
    c = pp(b.x, b.y);
    return dist(p, b);
  }
  return distToLine(p, a, b, c);
}
int n;
pair<double, double> p[N];
double dist(double x1, double y1, double x2, double y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
bool check(double mid) {
  for (int i = 0; i < n; i++) {
    for (int j = i + 1; j < n; j++) {
      double dd = dist(p[i].first, p[i].second, p[j].first, p[j].second);
      if (mid >= dd * 0.5) return false;
    }
  }
  for (int i = 0; i < n; i++) {
    int nxt = (i + 1) % n;
    int after = (i + 2) % n;
    pp c;
    pp a = pp(p[nxt].first, p[nxt].second);
    double distTo = distToLineSegment(a, pp(p[i].first, p[i].second),
                                      pp(p[after].first, p[after].second), c);
    if (mid > distTo * 0.5) return false;
  }
  return true;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    scanf("%lf%lf", &p[i].first, &p[i].second);
  }
  double lo = 0.0;
  double hi = 4e9;
  double mid = 0;
  for (int it = 0; it < 100; it++) {
    mid = (lo + hi) * 0.5;
    if (check(mid)) {
      lo = mid;
    } else {
      hi = mid;
    }
  }
  printf("%.9lf\n", mid);
  return 0;
}