Problem:
Score : 600 points

Problem Statement

Given are N points (x_i, y_i) in a two-dimensional plane.

Find the minimum radius of a circle such that all the points are inside or on it.

Constraints

2 \leq N \leq 50

0 \leq x_i \leq 1000

0 \leq y_i \leq 1000

The given N points are all different.

The values in input are all integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
:
x_N y_N

Output

Print the minimum radius of a circle such that all the N points are inside or on it.

Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

2
0 0
1 0

Sample Output 1

0.500000000000000000

Both points are contained in the circle centered at (0.5,0) with a radius of 0.5.

Sample Input 2

3
0 0
0 1
1 0

Sample Output 2

0.707106781186497524

Sample Input 3

10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9

Sample Output 3

6.726812023536805158

If the absolute or relative error from our answer is at most 10^{-6}, the output will be considered correct.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static double[][] a;
	static void Main(){
		Sc sc=new Sc();
		var n=sc.I;
		a=sc.Arr(n,()=>sc.Da);
		double lb=0,ub=long.MaxValue,mid=0;
		while(ub-lb>1e-11){
			mid=(ub+lb)/2;
			if(Fu(mid)){ub=mid;}
			else{lb=mid;}
		}
		Console.WriteLine("{0}",lb/2);
	}
	static bool Fu(double n){
		bool bo=true;
		for(int i = 0;i<a.Length;i++) {
			for(int j = i+1;j<a.Length;j++) {
				double d=Sqrt((a[i][0]-a[j][0])*(a[i][0]-a[j][0])+(a[i][1]-a[j][1])*(a[i][1]-a[j][1]));
				if(d>n){bo=false;}
			}
		}
		return bo;
	}
	static double Tst1(double a,double b){
		double lb=a,ub=b,c1=0,c2=0,d1=0,d2=0;
		while(ub-lb>1e-9){
			c1=(lb*2+ub)/3;
			c2=(lb+ub*2)/3;
			d1=Fu1(c1);
			d2=Fu1(c2);
			if(d1>d2){lb=c1;}
			else{ub=c2;}
		}
		return c1;
	}
	static double Tst2(double a,double b){
		double lb=a,ub=b,c1=0,c2=0,d1=0,d2=0;
		while(ub-lb>1e-9){
			c1=(lb*2+ub)/3;
			c2=(lb+ub*2)/3;
			d1=Fu2(c1);
			d2=Fu2(c2);
			if(d1>d2){lb=c1;}
			else{ub=c2;}
		}
		return c1;
	}
	static double Fu1(double p1){
		double d=0;
		for(int i = 0;i<a.Length;i++) {
			d=Max(d,Sqrt((a[i][0]-p1)*(a[i][0]-p1)));
		}
		return d;
	}
	static double Fu2(double p2){
		double d=0;
		for(int i = 0;i<a.Length;i++) {
			d=Max(d,Sqrt((a[i][1]-p2)*(a[i][1]-p2)));
		}
		return d;
	}
	static double Fu3(double p1,double p2){
		double d=0;
		for(int i = 0;i<a.Length;i++) {
			d=Max(d,Sqrt((a[i][0]-p1)*(a[i][0]-p1)+(a[i][1]-p2)*(a[i][1]-p2)));
		}
		return d;
	}
}
public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}