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<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<algorithm>
#include<cmath>
#include<climits>
#include<string>
#include<set>
#include<map>
#include<iostream>
using namespace std;
#define rep(i,n) for(int i=0;i<((int)(n));i++)
#define reg(i,a,b) for(int i=((int)(a));i<=((int)(b));i++)
#define irep(i,n) for(int i=((int)(n))-1;i>=0;i--)
#define ireg(i,a,b) for(int i=((int)(b));i>=((int)(a));i--)
typedef long long int lli;
typedef pair<int,int> mp;
#define fir first
#define sec second
#define IINF INT_MAX
#define LINF LLONG_MAX
#define eprintf(...) fprintf(stderr,__VA_ARGS__)
#define pque(type) priority_queue<type,vector<type>,greater<type> >
#define memst(a,b) memset(a,b,sizeof(a))
#define iter(v,ite) for(auto ite=(v).begin();ite!=(v).end();ite++)
#define mimunum(v,x) distance((v).begin(),lower_bound((v).begin(),(v).end(),x))


struct makehtml{
	vector<string> ss;
	
	makehtml(){}
	/*
	ctx.beginPath()
	ctx.moveTo(50.000000,100.000000);
	ctx.lineTo(150.000000,100.000000);
	ctx.stroke();
	
	ctx.fillStyle = "rgb(0,0,0)";
	
	ctx.beginPath();
	ctx.arc(168,59,3,0,360);
	ctx.fill();

	*/
	
	void out(const char* name,double mag){
		char fname[100];
		sprintf(fname,"%s.html",name);
		FILE* fp = fopen(fname,"w");
		if(fp==NULL){
			eprintf("can't open %s\b",fname);
			exit(-1);
		}
		fprintf(fp,"<html>\n<head>\n<title>");
		fprintf(fp,"%s",name);
		fprintf(fp,"</title>\n</head>\n<body>\n");
		fprintf(fp,"<p>name: %s</p>",name);
		fprintf(fp,"<canvas id=\"vis\" width=\"%d\" height=\"%d\"></canvas>",2000,2000);
		fprintf(fp,"<script>\n");
		fprintf(fp,"var vis = document.getElementById('vis');\nvar ctx = vis.getContext('2d');\n");
		
		rep(i,ss.size()){
			fprintf(fp,"%s\n",ss[i].c_str());
		}
		
		fprintf(fp,"</script>\n");
		fprintf(fp,"</body>\n</html>\n");
		fclose(fp);
	}

} makehtml_instance;

void addhtml(string s){
	makehtml_instance.ss.push_back(s);
}

void outhtml(string s,double mag){
	makehtml_instance.out(s.c_str(),mag);
}

void randcolhtml(){
	char ns[100];
	sprintf(ns,"ctx.fillStyle = \"rgb(%d,%d,%d)\";",rand()%128,rand()%128,rand()%128);
	addhtml(ns);
	sprintf(ns,"ctx.strokeStyle = \"rgb(%d,%d,%d)\";",rand()%128,rand()%128,rand()%128);
	addhtml(ns);
}

void inithtml(){
	makehtml_instance.ss.clear();
}


struct pos{
	double x,y;
	double norm,norm2;
	pos tov(pos a){
		return (a-(*this));
	}
	pos operator+(pos a)const{
		pos res=a;
		res.x+=x; res.y+=y;
		res=pos(res.x,res.y);
		return res;
	}
	pos operator-(pos a)const{
		pos res=(*this);
		res.x-=a.x; res.y-=a.y;
		res=pos(res.x,res.y);
		return res;
	}
	pos scalar(double a){
		pos res=(*this);
		res.x*=a; res.y*=a;
		res=pos(res.x,res.y);
		return res;
	}
	double dot(pos a){
		return x*a.x + y*a.y;
	}
	double cross(pos a){
		return x*a.y - y*a.x;
	}
	double theta(pos a){
		double nt=dot(a)/(norm*a.norm);
		nt=acos(max(-1.0,min(1.0,nt)));
		double ns=(cross(a)/(norm*a.norm));
		if(ns<0)nt*=-1;
		return nt;
	}
	pos(double ix,double iy){
		x=ix; y=iy;
		norm2=x*x+y*y;
		norm=sqrt(norm2);
	}
	pos(){}
	string str(){
		char ns[50];
		sprintf(ns,"(%lf %lf)",x,y);
		return	string(ns);
	}
	void outh(double mag){
		char ns[50];
		addhtml("ctx.beginPath();"); 
		sprintf(ns,"ctx.arc(%lf,%lf,%lf,0,360);",x*mag,y*mag,5.0); addhtml(ns);
		addhtml("ctx.fill();");
	}
	static pos polar(double r,double t){
		return pos(r*cos(t),r*sin(t));
	}
	bool  operator<(pos a) const{
		//if(x!=a.x)return (x<a.x);
		//return (y<a.y);
		if(y!=a.y)return (y<a.y);
		return (x<a.x);
	}	
	bool operator>(pos a)const{ return (a<(*this)); }	
};
struct line{
	pos p,q;
	pos vec;
	string str(){
		return ("("+p.str()+"-"+q.str()+")");
	}
	void outh(double mag){
		char ns[50];
		addhtml("ctx.beginPath();");
		sprintf(ns,"ctx.moveTo(%lf,%lf);",p.x*mag,p.y*mag); addhtml(ns);
		sprintf(ns,"ctx.lineTo(%lf,%lf);",q.x*mag,q.y*mag); addhtml(ns);
		addhtml("ctx.stroke();");
	}
	bool iscross(line a){
		double da,db;
		da=vec.cross( p.tov(a.p) );
		db=vec.cross( p.tov(a.q) );
		if(da*db>=0)return false;
		da=a.vec.cross( a.p.tov(p) );
		db=a.vec.cross( a.p.tov(q) );
		return (da*db<0);
	}
	line(pos ip,pos iq){
		p=ip; q=iq;
		vec=p.tov(q);
	}
	line(){}
	double dist(pos a){
		if(p.tov(a).dot( p.tov(q) )<0)return p.tov(a).norm;
		if(q.tov(a).dot( q.tov(p) )<0)return q.tov(a).norm;
		return abs(vec.cross(p.tov(a))/vec.norm);
	}
	double dist(line a){
		if(iscross(a))return 0;
		return min( min(dist(a.p),dist(a.q)) , min(a.dist(this->p),a.dist(this->q)));
	}
	pos crosspos(line a){
		/*
		double d1=a.vec.cross(a.p.tov(p))/a.vec.norm;
		double d2=a.vec.cross(a.p.tov(q))/a.vec.norm;
		bool isc=(d1*d2<0);
		d1=abs(d1); d2=abs(d2);
		double sc;
		if(!isc){
			if(d1>d2)sc = d1/(d1-d2);
			else sc=d1/(d2-d1);
		}
		else sc = d1/(d1+d2);
		return (p+vec.scalar(sc));*/
		
		double t = a.vec.cross(a.p-p)/a.vec.cross(vec);
		return (p+vec.scalar(t));
	}
	line bisection(){//?????´????????????
		//???????¨??????????90????????£???????????????
		pos fr=(p+q).scalar(0.5);
		pos to=fr+pos(-vec.y,vec.x);
		return line(fr,to);
	}
};
double lowofcos_getcos(double a,double b,double c){
	return ((a*a+b*b-c*c)/(2*a*b));
}
struct circle{
	pos p;
	double r;
	line koten(circle a){
		pos cv=p.tov(a.p);
		double br=atan2(cv.y,cv.x);
		double dr=acos(lowofcos_getcos( r, cv.norm, a.r));
		pos p1= p+pos::polar(r,br+dr);
		pos p2= p+pos::polar(r,br-dr);
		if(p1>p2)swap(p1,p2);
		return line(p1,p2);
	}
	circle(pos ip,double ir){
		p=ip; r=ir;
	}
	circle(){}
	void outh(double mag){
		char ns[50];
		addhtml("ctx.beginPath();"); 
		sprintf(ns,"ctx.arc(%lf,%lf,%lf,0,360);",p.x*mag,p.y*mag,r*mag); addhtml(ns);
		//addhtml("ctx.fill();");
	}
};

struct polygon{
	vector<pos> ps;
	polygon(){}
	void outh(double mag){
		char ns[50];
		addhtml("ctx.beginPath();");
		int ls=ps.size();
		sprintf(ns,"ctx.moveTo(%lf,%lf);",ps[ls-1].x*mag,ps[ls-1].y*mag); addhtml(ns);
		rep(i,ps.size()){
			sprintf(ns,"ctx.lineTo(%lf,%lf);",ps[i].x*mag,ps[i].y*mag); addhtml(ns);
		}
		addhtml("ctx.stroke();");
	}
	double area(){
		double res=0;
		rep(i,ps.size()){
			pos no=ps[i],to=ps[(i+1)%ps.size()];
			res+=(no.x+to.x)*(no.y-to.y);
		}
		if(res<0)reverse(ps.begin(),ps.end());
		return abs(res)/2;
	}
	polygon(pos a,pos b){
		ps.push_back(a);
		ps.push_back(pos(a.x,b.y));
		ps.push_back(b);
		ps.push_back(pos(b.x,a.y));
	}
	line gete(int a){
		a%=ps.size();
		return line(ps[a],ps[(a+1)%ps.size()]);
	}
	int isin(pos a){//?????´??????2,?????£????????????1,?????????0
		double as=0;
		rep(i,ps.size()){
			line ne=gete(i);
			if(ne.dist(a)<=0)return 1;
			pos v1=a.tov(ne.p);
			pos v2=a.tov(ne.q);
			as+=v1.theta(v2);
		}
		if(abs(as)<1e-6)return 0;
		return 2;
	}
	polygon convex_full(){
		polygon res;
		int ns=ps.size();
		vector<pos> vs(2*ns);
		sort(ps.begin(),ps.end());
		int k=0;
		rep(i,ns){
			pos np=ps[i];
			while(k>1 && vs[k-2].tov(vs[k-1]).cross(vs[k-1].tov(np))<-1e-6)k--;
			vs[k]=np; k++;
		}
		int t=k;
		ireg(i,0,ns-2){
			pos np=ps[i];
			while(k>t && vs[k-2].tov(vs[k-1]).cross(vs[k-1].tov(np))<-1e-6)k--;
			vs[k]=np; k++;
		}
		vs.resize(k-1);
		swap(vs,res.ps);
		return res;
	}
	polygon cut(line a){//???????????????????????????
		polygon res;
		rep(i,ps.size()){
			line ne=gete(i);
			double d1=a.vec.cross(a.p.tov(ne.p));
			double d2=a.vec.cross(a.p.tov(ne.q));
			if(d1<1e-6)res.ps.push_back(ne.p); //?????£????????£???eps
			if(d1*d2<-1e-6)res.ps.push_back(a.crosspos(ne)); //?????£????????????eps
		}
		return res;
	}
	
	vector<polygon> voronoi(vector<pos> ps){
		vector<polygon> res;
		rep(i,ps.size()){
			polygon np(*this);
			rep(j,ps.size()){
				if(i==j)continue;
				line nl = line(ps[j],ps[i]).bisection();
				
				np = np.cut(nl);
			}
			res.push_back(np);
		}
		return res;		
	}
	polygon mult(polygon a){
		return a;
	}
};

int main(void){
	for(;;){
		int n;
		scanf("%d",&n);
		if(n==0)break;
		polygon pol;
		rep(i,n){
			double x,y;
			scanf("%lf%lf",&x,&y);
			pol.ps.push_back(pos(x,y));
		}
		vector<line> es;
		rep(i,n)es.push_back(pol.gete(i));
		
		double l=0,r=1e6;
		rep(qqq,100){
			double d=(l+r)/2;
			polygon tp(pol);
			
			rep(i,n){
				line ne=es[i];
				pos bs=ne.bisection().vec;
				bs = bs.scalar(d/bs.norm);
				ne = line(ne.q+bs,ne.p+bs);
				tp = tp.cut(ne);
			}
			
			if(tp.ps.size()<=0)r=d;
			else l=d;
		}
		printf("%f\n",l);
	}
	return 0;
}