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 JAVA):

Solution:
import java.util.*;
import java.awt.geom.*;
import java.awt.geom.Point2D.Double;

import static java.lang.Math.*;
public class Main {
	final Scanner sc = new Scanner(System.in);
	public static void main(String[] args) {
		new Main().init();
	}
	void init(){
		new Q2007I();
	}
	
	Point2D intersectionPoint(Line2D l1,Line2D l2){
		return intersectionPoint(l1.getP1(), l1.getP2(), l2.getP1(), l2.getP2());
	}
	Point2D intersectionPoint(Point2D a1,Point2D a2,Point2D b1,Point2D b2){
		Point2D a=diff(a2,a1),
				b=diff(b2,b1);
		return sum(a1, mul(cross(b, diff(b1,a1))/cross(b,a), a));
	}
	Point2D diff(Point2D p1,Point2D p2){
		return new Point2D.Double(p1.getX()-p2.getX(), p1.getY()-p2.getY());
	}
	double cross(Point2D p1,Point2D p2){
		return p1.getX()*p2.getY() - p2.getX()*p1.getY();
	}
	Point2D mul(double n,Point2D p1){
		return new Point2D.Double(p1.getX()*n, p1.getY()*n);
	}
	Point2D sum(Point2D p1,Point2D p2){
		return new Point2D.Double(p1.getX()+p2.getX(), p1.getY()+p2.getY());
	}
	private ArrayList<Point2D> polygonCut(ArrayList<Point2D> plist, Line2D cut) {
		int n = plist.size();
		ArrayList<Point2D> ans = new ArrayList<Point2D>();
		for(int i =0; i<n; i++){
			Point2D from = plist.get(i), to = plist.get((i+1)%n);
			if(cut.relativeCCW(from) <= 0){
				ans.add(from);
			}
			int temp1 = cut.relativeCCW(from);
			int temp2 = cut.relativeCCW(to);
			if(temp1 * temp2 < 0){
				Point2D IntersectP = intersectionPoint(cut, new Line2D.Double(from,to));
				ans.add(IntersectP);
			}
		}
		return ans;
	}
	
	class Q2007I{
		int N;
		Q2007I(){
			while(true){
				N=sc.nextInt();
				if(N==0)	break;
				solve();
			}
		}
		void solve(){
			int[] x=new int[N],
					y=new int[N];
			for(int i=0; i<N; ++i){
				x[i]=sc.nextInt();
				y[i]=sc.nextInt();
			}
			
			double ret = f1(x,y);
			System.out.printf("%.7f\n" ,ret);
			
		}
		final double EPS = 1.0e-7;
		double f1(int[] x,int[] y){
			double l=0, r=30000;
			while(abs(r-l) > EPS){
				double mid = (l+r)/2;
				ArrayList<Point2D> tmp = new ArrayList<Point2D>(N);
				for(int i=0; i<N; ++i){
					tmp.add(new Point2D.Double(x[i], y[i]));
				}
				boolean flg = f2(tmp, mid);	// true = 沈む false = 残る
				if(flg)	r=mid;
				else	l=mid;
			}
			return r;
		}
		
		boolean f2(ArrayList<Point2D> ps, double d){
			
			Line2D.Double[] cuts = new Line2D.Double[ps.size()];
			for(int i=0; i<ps.size(); ++i){
				Point2D p1 = ps.get(i),
						p2 = ps.get((i+1)%ps.size());
				double x = -(p2.getY()-p1.getY()),
						y = (p2.getX()-p1.getX());
				double d2 = p1.distance(p2);
				x = x*d/d2;	y=y*d/d2;
				Point2D v1 = new Point2D.Double(x,y);
				cuts[i] = new Line2D.Double(sum(p1, v1), sum(p2, v1));
			}
			
			for(Line2D.Double cut: cuts){
				ps = polygonCut(ps, cut);
			}
			
//			System.out.println("D:"+d+" ps:"+ps.size());
			
			return ps.isEmpty();
			
		}
	}
}