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"

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

using namespace std;

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std
{
bool operator<(const Point &lhs, const Point &rhs)
{
    if (lhs.real() < rhs.real() - eps)
        return true;
    if (lhs.real() > rhs.real() + eps)
        return false;
    return lhs.imag() < rhs.imag();
}
} // namespace std

Point input_point()
{
    ld x, y;
    cin >> x >> y;
    return Point(x, y);
}

bool eq(ld a, ld b)
{
    return (abs(a - b) < eps);
}

ld dot(Point a, Point b)
{
    return real(conj(a) * b);
}

ld cross(Point a, Point b)
{
    return imag(conj(a) * b);
}

class Line
{
  public:
    Point a, b;
    Line() : a(Point(0, 0)), b(Point(0, 0)) {}
    Line(Point a, Point b) : a(a), b(b) {}
};

class Circle
{
  public:
    Point p;
    ld r;
    Circle() : p(Point(0, 0)), r(0) {}
    Circle(Point p, ld r) : p(p), r(r) {}
};

// CCW::counter clockwise
int ccw(Point a, Point b, Point c)
{
    b -= a;
    c -= a;
    if (cross(b, c) > eps)
        return 1; // a,b,c : counter-clockwise
    if (cross(b, c) < -eps)
        return -1; // a,b,c : clockwise
    if (dot(b, c) < 0)
        return 2; // c,a,b : on a line
    if (norm(b) < norm(c))
        return -2; // a,b,c : on a line
    return 0;      // a,c,b : on a line
}

bool isis_ll(Line l, Line m)
{
    return !eq(cross(l.b - l.a, m.b - m.a), 0);
}

// s : line segment
bool isis_ls(Line l, Line s)
{
    return isis_ll(l, s) &&
           (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

bool isis_ss(Line s, Line 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 isis_lp(Line l, Point p)
{
    return (abs(cross(l.b - p, l.a - p)) < eps);
}

bool isis_sp(Line s, Point p)
{
    return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

Point proj(Line l, Point p)
{
    ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}

Point is_ll(Line s, Line t)
{
    Point sv = s.b - s.a, tv = t.b - t.a;
    assert(cross(sv, tv) != 0);
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

ld dist_lp(Line l, Point p)
{
    return abs(p - proj(l, p));
}

ld dist_ll(Line l, Line m)
{
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

ld dist_ls(Line l, Line s)
{
    return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p)
{
    Point r = proj(s, p);
    return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t)
{
    if (isis_ss(s, t))
        return 0;
    return min({dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

vector<Point> is_cc(Circle c1, Circle c2)
{
    vector<Point> res;
    ld d = abs(c1.p - c2.p);
    ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
    ld dfr = c1.r * c1.r - rc * rc;
    if (abs(dfr) < eps)
        dfr = 0.0;
    else if (dfr < 0.0)
        return res; // no intersection
    ld rs = sqrt(dfr);
    Point diff = (c2.p - c1.p) / d;
    res.push_back(c1.p + diff * Point(rc, rs));
    if (dfr != 0.0)
        res.push_back(c1.p + diff * Point(rc, -rs));
    return res;
}

vector<Point> is_lc(Circle c, Line l)
{
    vector<Point> res;
    ld d = dist_lp(l, c.p);
    if (d < c.r + eps)
    {
        ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d); //safety;
        Point nor = (l.a - l.b) / abs(l.a - l.b);
        res.push_back(proj(l, c.p) + len * nor);
        res.push_back(proj(l, c.p) - len * nor);
    }
    return res;
}

vector<Point> is_sc(Circle c, Line l)
{
    vector<Point> v = is_lc(c, l), res;
    for (Point p : v)
        if (isis_sp(l, p))
            res.push_back(p);
    return res;
}

vector<Line> tangent_cp(Circle c, Point p)
{
    vector<Line> ret;
    Point v = c.p - p;
    ld d = abs(v);
    ld l = sqrt(norm(v) - c.r * c.r);
    if (isnan(l))
    {
        return ret;
    }
    Point v1 = v * Point(l / d, c.r / d);
    Point v2 = v * Point(l / d, -c.r / d);
    ret.push_back(Line(p, p + v1));
    if (l < eps)
        return ret;
    ret.push_back(Line(p, p + v2));
    return ret;
}

vector<Line> tangent_cc(Circle c1, Circle c2)
{
    vector<Line> ret;
    if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps)
    {
        Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
        ret = tangent_cp(c1, center);
    }
    if (abs(c1.r - c2.r) > eps)
    {
        Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
        vector<Line> nret = tangent_cp(c1, out);
        ret.insert(ret.end(), ALL(nret));
    }
    else
    {
        Point v = c2.p - c1.p;
        v /= abs(v);
        Point q1 = c1.p + v * Point(0, 1) * c1.r;
        Point q2 = c1.p + v * Point(0, -1) * c1.r;
        ret.push_back(Line(q1, q1 + v));
        ret.push_back(Line(q2, q2 + v));
    }
    return ret;
}

// a, b の垂直二等分線. a -> b を90度反時計回り回転
Line bisector(Point a, Point b)
{
    Point mid = (a + b) * Point(0.5, 0);
    return Line(mid, mid + (b - a) * Point(0, pi / 2));
}

typedef vector<Point> Polygon;

ld area(const Polygon &p)
{
    ld res = 0;
    int n = p.size();
    REP(j, n)
    res += cross(p[j], p[(j + 1) % n]);
    return res / 2;
}

bool is_counter_clockwise(const Polygon &poly)
{
    ld angle = 0;
    int n = poly.size();
    REP(i, n)
    {
        Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
        angle += arg((c - b) / (b - a));
    }
    return angle > eps;
}

// -1 => out
//  0 => on
//  1 => in
int is_in_polygon(const Polygon &poly, Point p)
{
    ld angle = 0;
    int n = poly.size();
    REP(i, n)
    {
        Point a = poly[i], b = poly[(i + 1) % n];
        if (isis_sp(Line(a, b), p))
            return 1;
        angle += arg((b - p) / (a - p));
    }
    return eq(angle, 0) ? 0 : 2;
}

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

Polygon convex_cut(const Polygon &ps, Line l)
{
    int n = ps.size();
    Polygon Q;
    REP(i, n)
    {
        Point A = ps[i], B = ps[(i + 1) % n];
        Line m = Line(A, B);
        if (ccw(l.a, l.b, A) != -1)
            Q.push_back(A);
        if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
            Q.push_back(is_ll(l, m));
    }
    return Q;
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    while (cin >> N, N)
    {
        Polygon land;
        for (int i = 0; i < N; i++)
        {
            ld x, y;
            cin >> x >> y;
            land.push_back(Point(x, y));
        }
        ld low = 0, high = 100000;
        for (int k = 0; k < 100; k++)
        {
            ld mid = (low + high) / 2;
            Polygon p = land;
            for (int i = 0; i < N; i++)
            {
                Point a = land[i], b = land[(i + 1) % N];
                Point st = a + (mid / abs(b - a)) * ((b - a) * Point(0, 1)), gt = st + (b - a);
                p = convex_cut(p, Line(st, gt));
            }
            if (p.size() == 0)
            {
                high = mid;
            }
            else
            {
                low = mid;
            }
        }
        cout << fixed << setprecision(10) << low << endl;
    }
}