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;

#define rep(i,x,y) for(int i=(x);i<(y);++i)
#define debug(x) #x << "=" << (x)

#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define show(x) std::cerr << debug(x) << " (L:" << __LINE__ << ")" << std::endl
#else
#define show(x)
#endif

typedef long long int ll;
typedef pair<int,int> pii;
template<typename T> using vec=std::vector<T>;

const int inf=1<<30;
const long long int infll=1LL<<62;
const double eps=1e-9;
const int dx[]={1,0,-1,0},dy[]={0,1,0,-1};

template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec){
    os << "[";
    for (const auto &v : vec) {
    	os << v << ",";
    }
    os << "]";
    return os;
}

typedef complex<long double> point;
typedef pair<point,point> line;
bool equal(const long double x1,const long double x2){ return abs(x1-x2)<eps; }
bool equal(const point& a,const point& b){ return equal(a.real(),b.real()) and equal(a.imag(),b.imag()); }
long double length(const point& a){ return abs(a); }
long double distance(const point& a,const point& b){ return abs(a-b); }
long double dot(const point& a,const point& b){ return a.real()*b.real()+a.imag()*b.imag(); }
long double cross(const point& a,const point& b){ return a.real()*b.imag()-a.imag()*b.real(); }
bool is_orthogonal(const point& a1,const point& a2,const point& b1,const point& b2){ return equal(dot(a1-a2,b1-b2),0.0); }
bool is_orthogonal(const line& l,const line& m){ return is_orthogonal(l.first,l.second,m.first,m.second); }
bool is_parallel(const point& a1,const point& a2,const point& b1,const point& b2){ return equal(cross(a1-a2, b1-b2),0.0); }
bool is_parallel(const line& l,const line& m){ return is_parallel(l.first,l.second,m.first,m.second); }
int ccw(point a,point b,point c) {
    b-=a; c-=a;
    if(cross(b, c) > 0)   return +1;       // counter clockwise
    if(cross(b, c) < 0)   return -1;       // clockwise
    if(dot(b, c) < 0)     return +2;       // c--a--b on line
    if(norm(b) < norm(c)) return -2;       // a--b--c on line
    return 0;
}
bool intersectLL(const line& l, const line& m){
    return abs(cross(l.second-l.first, m.second-m.first)) > eps || // non-parallel
           abs(cross(l.second-l.first, m.first-l.first)) < eps;   // same line
}
bool intersectLS(const line& l, const line& s){
    return cross(l.second-l.first, s.first-l.first)*       // s.first is left of l
           cross(l.second-l.first, s.second-l.first) < eps; // s.second is right of l
}
bool intersectLP(const line& l, const point& p){
    return abs(cross(l.second-p, l.first-p)) < eps;
}
bool intersectSS(const line& s, const line& t){
    return ccw(s.first,s.second,t.first)*ccw(s.first,s.second,t.second) <= 0 &&
           ccw(t.first,t.second,s.first)*ccw(t.first,t.second,s.second) <= 0;
}
bool intersectSP(const line& s, const point& p){
    return abs(s.first-p)+abs(s.second-p)-abs(s.second-s.first) < eps; // triangle inequality
}
point projection(const line& l, const point& p) {
    long double t = dot(p-l.first, l.first-l.second) / norm(l.first-l.second);
    return l.first + t*(l.first-l.second);
}
point reflection(const line& l, const point& p){
    return p+point((projection(l, p) - p).real()*2,(projection(l, p) - p).imag()*2);
}
long double distanceLP(const line &l, const point& p){
    return abs(p - projection(l, p));
}
long double distanceLL(const line &l, const line &m){
    return intersectLL(l, m) ? 0 : distanceLP(l, m.first);
}
long double distanceLS(const line &l, const line &s){
    if (intersectLS(l, s)) return 0;
    return min(distanceLP(l, s.first), distanceLP(l, s.second));
}
long double distanceSP(const line &s, const point& p) {
    const point r = projection(s, p);
    if (intersectSP(s, r)) return abs(r - p);
    return min(abs(s.first - p), abs(s.second - p));
}
long double distanceSS(const line &s, const line &t) {
    if (intersectSS(s, t)) return 0;
    return min(min(distanceSP(s, t.first), distanceSP(s, t.second)),
             min(distanceSP(t, s.first), distanceSP(t, s.second)));
}
// a1,a2???????????´?????¨b1,b2???????????´?????????????¨????
point intersection_l(const point& a1,const point& a2,const point& b1,const point& b2) {
  const point& a=a2-a1,b=b2-b1;
  return a1+a*cross(b, b1-a1)/cross(b, a);
}
point intersection_l(const line& l,const line& m){
    return intersection_l(l.first,l.second,m.first,m.second);
}
// ????§???¢????¬?????????¢???
long double area(const vector<point>& pol){
    long double s=0;
    rep(i,0,pol.size()) s+=cross(pol[i],pol[(i+1)%pol.size()]);
    return s/2;
}

//??´??????????????????????????????????±???????
line get_unit_normalV(const point &a,const point &b){
    line l;
    l.first=((b-a)*point(0,1))/abs(b-a);
    l.second=((b-a)*point(0,-1))/abs(b-a);
    return l;
}

//??????s????????¢d?????????????§????
pair<line,line> get_translation(const line &s,long double d){
    line v = get_unit_normalV(s.first,s.second);
    pair<line,line> res;
    res.first=line(s.first+v.first*d,s.second+v.first*d);
    res.second=line(s.first+v.second*d,s.second+v.second*d);
    return res;
}

vector<point> convex_cut(const vector<point>& ps, const line& l) {
    vector<point> res;
    for (int i = 0; i < ps.size(); ++i) {
        point a = ps[i], b = ps[(i+1)%ps.size()];
        if (ccw(l.first, l.second, a) != -1) res.push_back(a);
        if (ccw(l.first, l.second, a)*ccw(l.first, l.second, b) < 0) res.push_back(intersection_l(line(a, b), l));
    }
    return res;
}

void solve(int n){
    vector<point> ps;
    rep(i,0,n){
        long double x,y;
        cin >> x >> y;
        ps.push_back(point(x,y));
    }
    ps.push_back(ps[0]);
    vector<line> ls;
    rep(i,0,n) ls.push_back(line(ps[i],ps[i+1]));

    auto ok=[&](long double k){
        vector<point> pol;
        rep(i,0,n) pol.push_back(ps[i]);
        rep(i,0,n){
            auto tl=get_translation(ls[i],k);
            if(ccw(ps[i],ps[i+1],tl.first.first)==1) pol=convex_cut(pol,tl.first);
            else pol=convex_cut(pol,tl.second);
        }
        return pol.size()>0;
    };

    long double lb=0,ub=inf;
    rep(i,0,64){
        long double m=(lb+ub)/2;
        if(ok(m)) lb=m;
        else ub=m;
    }
    cout << lb << endl;
}

int main(){
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    cout.setf(ios::fixed);
    cout.precision(10);
    while(true){
        int n;
        cin >> n;
        if(!n) break;
        solve(n);
    }
    return 0;
}