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;

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=a;i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(a>b)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

using ld=long double;
using cm=complex<ld>;
#define x real()
#define y imag()
const ld eps=1e-8;
const ld PI=acos(ld(-1));
int sgn(ld a){return a<-eps?-1:(a>eps?1:0);}
ld dot(cm a,cm b){return a.x*b.x+a.y*b.y;}
ld crs(cm a,cm b){return a.x*b.y-a.y*b.x;}
ld crs(cm a,cm b,cm c){return crs(b-a,c-a);}
int ccw(cm a,cm b){return sgn(crs(a,b));}
int ccw(cm a,cm b,cm c){return ccw(b-a,c-a);}
auto cmcmp=[](cm a,cm b){
	if(sgn(a.x-b.x))return a.x<b.x;
	else return sgn(a.y-b.y)<0;
};
bool cmeq(cm a,cm b){
	return sgn(a.x-b.x)==0&&sgn(a.y-b.y)==0;
};
//(-pi,0](0,pi]
int argtype(cm a){
	if(sgn(a.y)==0)return a.x<0?1:0;
	return a.y<0?0:1;
}
int argcmp(cm a,cm b){
	int at=argtype(a),bt=argtype(b);
	if(at!=bt)return sgn(at-bt);
	return -ccw(a,b);
};
//AOJ1183
int qeq(ld a,ld b,ld c,ld&d,ld&e){
	ld f=b*b-4*a*c;
	if(sgn(f)<0)return 0;
	ld g=sqrt(max(f,ld(0)));
	d=(-b+g)/(2*a);
	e=(-b-g)/(2*a);
	return sgn(f)+1;
}
//(-2)[a,-1](0)[b,1](2)
int bet(cm a,cm b,cm c){
	cm d=b-a;
	ld e=dot(d,c-a);
	if(sgn(e)<=0)return sgn(e)-1;
	return sgn(e-norm(d))+1;
}
//AOJ0153
//0-no,1-edge,2-in
int cont(cm a,cm b,cm c,cm d){
	if(ccw(a,b,c)==-1)
		swap(b,c);
	return min({ccw(a,b,d),ccw(b,c,d),ccw(c,a,d)})+1;
}
//AOJ1183
//arg between ab
//assume given lengths are valid
ld arg(ld a,ld b,ld c){
	return acos(min(max((a*a+b*b-c*c)/(2*a*b),ld(-1)),ld(1)));
}
//AOJ2233
//a->b->c と進むときに曲がる角度
//a-b-cが一直線上にあれば0が帰る
ld turn(cm a,cm b,cm c){
	return arg((c-b)/(b-a));
}

using ln=pair<cm,cm>;
cm dir(ln a){return a.b-a.a;}
cm eval(ln a,ld b){return a.a+dir(a)*b;}
int bet(ln a,cm b){return bet(a.a,a.b,b);}
int ccw(ln a,cm b){return ccw(a.a,a.b,b);}
cm proj(ln a,cm b){
	cm c=dir(a);
	return a.a+c*dot(c,b-a.a)/norm(c);
}
cm refl(ln a,cm b){
	return ld(2)*proj(a,b)-b;
}
//AOJ0153
ld dsp(ln a,cm b){
	cm c=proj(a,b);
	if(abs(bet(a.a,a.b,c))<=1)return abs(b-c);
	return min(abs(b-a.a),abs(b-a.b));
}
//AOJ1157
//0-no,1-yes(endpoint),2-yes(innner),3-overelap
int iss(ln a,ln b){
	int c1=ccw(a.a,a.b,b.a),c2=ccw(a.a,a.b,b.b);
	int d1=ccw(b.a,b.b,a.a),d2=ccw(b.a,b.b,a.b);
	if(c1||c2||d1||d2)return 1-max(c1*c2,d1*d2);
	int f=bet(a.a,a.b,b.a),g=bet(a.a,a.b,b.b);
	if(max(f,g)==-2||min(f,g)==2)return 0;
	return 3;
}
//AOJ1033
cm cll(ln a,ln b){
	return eval(a,crs(b.a,b.b,a.a)/crs(dir(a),dir(b)));
}
//AOJ1157
ld dss(ln a,ln b){
	if(iss(a,b))return 0;
	return min({dsp(a,b.a),dsp(a,b.b),dsp(b,a.a),dsp(b,a.b)});
}
//AOJ2160
//反時計回り方向に伸びる垂直二等分線
ln vbis(cm a,cm b){
	cm c=(a+b)*ld(0.5),d=b-a;
	return ln(c,cm(c.x-d.y,c.y+d.x));
}

//convex cut
vc<cm> ccut(vc<cm> a,ln b){
	int n=a.size();
	vc<cm> c;
	rep(i,n){
		int j=(i+1)%n;
		int d=ccw(b,a[i]),e=ccw(b,a[j]);
		if(d>=0)c.pb(a[i]);
		if(d*e<0)c.pb(cll(b,ln(a[i],a[j])));
	}
	return c;
}

signed main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(20);
	
	while(1){
		int n;cin>>n;
		if(n==0)break;
		vc<cm> a;
		rep(i,n){
			ld s,t;
			cin>>s>>t;
			a.eb(s,t);
		}
		
		ld lw=0,up=100000;
		rep(_,80){
			ld mid=(lw+up)/2;
			vc<cm> b=a;
			rep(i,n){
				cm c=a[i],d=a[(i+1)%n];
				cm e=d-c;
				e=cm(-e.y,e.x);
				e*=mid/abs(e);
				b=ccut(b,ln(c+e,d+e));
			}
			if(b.size())
				lw=mid;
			else
				up=mid;
		}
		cout<<lw<<endl;
	}
}