Problem: The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it is natural to ask a question: "Where is the most distant point from the sea?" The answer to this question for Honshu was found in 1996. The most distant point is located in former Usuda Town, Nagano Prefecture, whose distance from the sea is 114.86 km.

In this problem, you are asked to write a program which, given a map of an island, finds the most distant point from the sea in the island, and reports its distance from the sea. In order to simplify the problem, we only consider maps representable by convex polygons.



Input

The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.


n
x1    y1
.
.
.
xn    yn


Every input item in a dataset is a non-negative integer. Two input items in a line are separated by a space.

n in the first line is the number of vertices of the polygon, satisfying 3 ≤ n ≤ 100. Subsequent n lines are the x- and y-coordinates of the n vertices. Line segments (xi, yi) - (xi+1, yi+1) (1 ≤ i ≤ n - 1) and the line segment (xn, yn) - (x1, y1) form the border of the polygon in counterclockwise order. That is, these line segments see the inside of the polygon in the left of their directions. All coordinate values are between 0 and 10000, inclusive.

You can assume that the polygon is simple, that is, its border never crosses or touches itself. As stated above, the given polygon is always a convex one.

The last dataset is followed by a line containing a single zero.

Output

For each dataset in the input, one line containing the distance of the most distant point from the sea should be output. An output line should not contain extra characters such as spaces.

The answer should not have an error greater than 0.00001 (10-5 ). You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.

Example

Input

4
0 0
10000 0
10000 10000
0 10000
3
0 0
10000 0
7000 1000
6
0 40
100 20
250 40
250 70
100 90
0 70
3
0 0
10000 10000
5000 5001
0


Output

5000.000000
494.233641
34.542948
0.353553

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

const double EPS = 1e-8, PI = acos(-1);

inline bool eq(double a, double b) { return abs(b - a) < EPS; }

#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
enum
{
  OUT, ON, IN
};
namespace Geometory
{
  struct Point
  {
    double x, y;

    Point() {};

    Point(double x, double y) : x(x), y(y) {};

    Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }

    Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }

    Point operator*(const double b) const { return Point(x * b, y * b); }

    Point operator*(const Point &b) const { return Point(x * b.x - y * b.y, x * b.y + y * b.x); }

    Point operator/(const double b) const { return Point(x / b, y / b); }

    bool operator<(const Point &b) const { return x != b.x ? x < b.x : y < b.y; }

    bool operator==(const Point &b) const { return eq(x, b.x) && eq(y, b.y); }

    double norm() { return x * x + y * y; }

    double arg() { return atan2(x, y); }

    double abs() { return sqrt(norm()); }

    Point rotate(double theta) { return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y); }

    Point rotate90() { return Point(-y, x); }

    friend ostream &operator<<(ostream &os, Point &p) { return os << "(" << p.x << "," << p.y << ")"; }

    friend istream &operator>>(istream &is, Point &a) { return is >> a.x >> a.y; }
  };

  struct Line
  {
    Point a, b;

    Line() {};

    Line(Point a, Point b) : a(a), b(b) {};

    friend ostream &operator<<(ostream &os, Line &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }

    friend istream &operator>>(istream &is, Line &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };

  struct Segment
  {
    Point a, b;

    Segment() {};

    Segment(Point a, Point b) : a(a), b(b) {};

    friend ostream &operator<<(ostream &os, Segment &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }

    friend istream &operator>>(istream &is, Segment &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };

  struct Circle
  {
    Point p;
    double r;

    Circle() {};

    Circle(Point p, double r) : p(p), r(r) {};
  };

  typedef vector< Point > Polygon;
  typedef vector< Segment > Segments;
  typedef vector< Line > Lines;
  typedef vector< Circle > Circles;
  typedef pair< Point, Point > PointPoint;

  double cross(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;
  }

  int ccw(const Point &a, Point b, Point c)
  {
    b = b - a, c = c - a;
    if(cross(b, c) > EPS) return +1;  // a ??? b ???§ ????????¨??????????????????? c
    if(cross(b, c) < -EPS) return -1; // a ??? b ???§ ?????¨??????????????????? c
    if(dot(b, c) < 0) return +2;  // c -- a -- b???§??????´??????
    if(b.norm() < c.norm()) return -2; // a -- b -- c???§??????´??????
    return 0;  // a -- c -- b???§??????´??????
  }

  Point Projection(const Line &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }

  Point Projection(const Segment &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }

  Point Reflection(const Line &l, const Point &p)
  {
    return p + (Projection(l, p) - p) * 2.0;
  }

  double Distance(const Line &l, const Point &p)
  {
    return (p - Projection(l, p)).abs();
  }

  bool Intersect(const Line &l, const Line &m)
  {
    return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;
  }

  bool Intersect(const Line &l, const Segment &s)
  {
    return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
  }

  bool Intersect(const Line &l, const Point &p)
  {
    return abs(ccw(l.a, l.b, p)) != -1;
  }

  bool Intersect(const Segment &s, const Segment &t)
  {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
  }

  bool Intersect(const Segment &s, const Point &p)
  {
    return ccw(s.a, s.b, p) == 0;
  }

  bool Intersect(const Circle &c, const Line &l)
  {
    return Distance(l, c.p) <= c.r + EPS;
  }

  bool Intersect(const Circle &c, const Point &p)
  {
    return abs((p - c.p).abs() - c.r) < EPS;
  }

  int Intersect(const Circle &c, const Segment &l)
  {
    if((Projection(l, c.p) - c.p).norm() - c.r * c.r > EPS) return 0;
    const double d1 = (c.p - l.a).abs(), d2 = (c.p - l.b).abs();
    if(d1 < c.r + EPS && d2 < c.r + EPS) return 0;
    if(d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS) return 1;
    const Point h = Projection(l, c.p);
    if(dot(l.a - h, l.b - h) < 0) return 2;
    return 0;
  }

  bool Intersect(const Circle &a, const Circle &b)
  {
    return ((a.p - b.p).norm() - (a.r + b.r) * (a.r + b.r) < EPS) &&
           ((a.p - b.p).norm() - (a.r - b.r) * (a.r - b.r) > -EPS);
  }

  double Distance(const Segment &s, const Point &p)
  {
    Point r = Projection(s, p);
    if(Intersect(s, r)) return (r - p).abs();
    return min((s.a - p).abs(), (s.b - p).abs());
  }

  double Distance(const Segment &a, const Segment &b)
  {
    if(Intersect(a, b)) return 0;
    return min(min(Distance(a, b.a), Distance(a, b.b)), min(Distance(b, a.a), Distance(b, a.b)));
  }

  double Distance(const Line &l, const Line &m)
  {
    return Intersect(l, m) ? 0 : Distance(l, m.a);
  }

  double Distance(const Line &l, const Segment &s)
  {
    if(Intersect(l, s)) return 0;
    return min(Distance(l, s.a), Distance(l, s.b));
  }

  double Distance(const Point &a, const Point &b)
  {
    return (a - b).abs();
  }

  Point Crosspoint(const Line &l, const Line &m)
  {
    double A = cross(l.b - l.a, m.b - m.a);
    double B = cross(l.b - l.a, l.b - m.a);
    if(abs(A) < EPS && abs(B) < EPS) return m.a; // same line
    return m.a + (m.b - m.a) * B / A;
  }

  Point Crosspoint(const Segment &l, const Segment &m)
  {
    double A = cross(l.b - l.a, m.b - m.a);
    double B = cross(l.b - l.a, l.b - m.a);
    if(abs(A) < EPS && abs(B) < EPS) return m.a; // same line
    return m.a + (m.b - m.a) * B / A;
  }

  PointPoint Crosspoint(const Circle &c, const Line l)
  {
    Point hp = Projection(l, c.p), h = hp - c.p;
    const double d2 = h.norm();
    Point v = (l.b - l.a) * sqrt(c.r * c.r - d2) / (l.b - l.a).abs();
    return PointPoint(hp - v, hp + v);
  }

  PointPoint Crosspoint(const Circle &c, const Segment &l)
  {
    Line aa = Line(l.a, l.b);
    if(Intersect(c, l) == 2) return Crosspoint(c, aa);
    PointPoint ret = Crosspoint(c, aa);
    if(dot(l.a - ret.first, l.b - ret.first) < 0) ret.second = ret.first;
    else ret.first = ret.second;
    return ret;
  }

  PointPoint Crosspoint(const Circle &c1, const Circle &c2)
  { //OK
    double d = (c1.p - c2.p).abs();
    double s = (c1.r + c2.r + d) / 2;
    double S = sqrt(s * (s - c1.r) * (s - c2.r) * (s - d));
    double h = 2 * S / d;
    Point v = (c2.p - c1.p) / (c2.p - c1.p).abs();
    double m = sqrt(c1.r * c1.r - h * h);
    return PointPoint(c1.p + v * m + Point(0, 1) * h * v, c1.p + v * m - Point(0, 1) * h * v);
  }

  bool parallel(const Line &a, const Line &b)
  {
    return abs(cross(a.b - a.a, b.b - b.a)) < EPS;
  }

  bool orthogonal(const Line &a, const Line &b)
  {
    return abs(dot(a.a - a.b, b.a - b.b)) < EPS;
  }

  int Contains(const Polygon &Q, const Point &p)
  {
    bool in = false;
    for(int i = 0; i < Q.size(); i++) {
      Point a = curr(Q, i) - p, b = next(Q, i) - p;
      if(a.y > b.y) swap(a, b);
      if(a.y <= 0 && 0 < b.y && cross(a, b) < 0) in = !in;
      if(cross(a, b) == 0 && dot(a, b) <= 0) return ON;
    }
    return in ? IN : OUT;
  }

  bool Contains(const Circle &c, const Point &p)
  {
    return (c.p - p).abs() < c.r + EPS;
  }

  double Area2(const Polygon &p)
  { //OK
    double A = 0;
    for(int i = 0; i < p.size(); ++i) {
      A += cross(curr(p, i), next(p, i));
    }
    return A;
  }

  bool IsConvex(const Polygon &p)
  {
    for(int i = 0; i < p.size(); i++) {
      if(ccw(prev(p, i), curr(p, i), next(p, i)) == -1) return false;
    }
    return true;
  }

  Polygon Convex_Hull(Polygon &p)
  {
    int n = p.size(), k = 0;
    if(n >= 3) {
      sort(p.begin(), p.end());
      vector< Point > ch(2 * n);
      for(int i = 0; i < n; ch[k++] = p[i++]) {
        while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
        while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      ch.resize(k - 1);
      return ch;
    } else {
      return p;
    }
  }

  double Convex_Diameter(Polygon &p)
  {
    int n = p.size();
    int is = 0, js = 0;
    for(int i = 1; i < n; i++) {
      if(p[i].y > p[is].y) is = i;
      if(p[i].y < p[js].y) js = i;
    }
    double maxdis = (p[is] - p[js]).norm();

    int maxi, maxj, i, j;
    i = maxi = is;
    j = maxj = js;
    do {
      if(cross(next(p, i) - curr(p, i), next(p, j) - curr(p, j)) >= 0) {
        j = (j + 1) % n;
      } else {
        i = (i + 1) % n;
      }
      if((p[i] - p[j]).norm() > maxdis) {
        maxdis = (p[i] - p[j]).norm();
        maxi = i;
        maxj = j;
      }
    } while(i != is || j != js);
    return maxdis;
  }

  Line Bisector(Point a, Point b)
  {
    Point c = (a + b) * 0.5;
    Point p = Point(c.x + (a.y - b.y), c.y + (b.x - a.x));
    return (Line(c, p));
  }

  Polygon Convex_Cut(Polygon &U, Line l)
  {
    Polygon ret;
    for(int i = 0; i < U.size(); i++) {
      Point now = curr(U, i), nxt = next(U, i);
      if(ccw(l.a, l.b, now) != -1) ret.push_back(now);
      if(ccw(l.a, l.b, now) * ccw(l.a, l.b, nxt) < 0) {
        ret.push_back(Crosspoint(Line(now, nxt), l));
      }
    }
    return (ret);
  }
};

using namespace Geometory;

Polygon data;

bool isable(double v)
{
  Polygon ret = data;
  for(int i = 0; i < data.size(); i++) {
    Point point = next(data, i) - curr(data, i);
    point = (point * v / point.abs()).rotate(PI / 2);
    ret = Convex_Cut(ret, Line(curr(data, i) + point, next(data, i) + point));
  }
  return (!ret.empty());
}

int main()
{
  int N;
  cout << fixed << setprecision(10);
  while(cin >> N, N) {
    data.resize(N);
    for(int i = 0; i < N; i++) cin >> data[i];
    double low = 0, high = 1e4;
    for(int i = 0; i < 40; i++) {
      double mid = (low + high) * 0.5;
      if(isable(mid)) low = mid;
      else high = mid;
    }
    cout << low << endl;
  }

}