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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		int i = 0;
//		int t = in.nextInt();
//		for (; i < t; i++)
		solver.solve(i, in, out);

		out.close();

	}

	static class Task {

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			ArrayList<Point> al=new ArrayList<Point>();
			ArrayList<Double> d=new ArrayList<Double>();
			for (int i = 0; i < n; i++) {
				al.add(new Point(in.nextDouble(),in.nextDouble()));
			}
			for (int i = 0; i < n; i++) {
				for (int j = i+1; j < n; j++) {
					Point mp = al.get(i).mp(al.get(j));
					double dt=mp.d(al.get(i));
					boolean flag=false;
					for (int k = 0; k < n; k++) {
						if(al.get(k).d(mp)>dt) {
							flag=true;
							break;
						}
					}
					if(!flag) {
						d.add(dt);
					}
				}
			}
			try {
				
			d.sort(null);
			System.out.println(d.get(0));
			}catch(Exception e) {
				
			}
			
			
			
		}

		private void leastmoves(int i, int j, int[][] data) {
			// TODO Auto-generated method stub
			
		}

		static long modInverse(long a, int m) {
			long g = gcd(a, m);
			if (g != 1) {
				System.out.println("Inverse doesn't exist");
				return 0;
			} else {
				// If a and m are relatively prime, then modulo inverse
				// is a^(m-2) mode m
				return power(a, m - 2, m);
			}
		}

		// To compute x^y under modulo m
		static long power(long x, long y, long m) {
			if (y == 0)
				return 1;

			long p = power(x, y / 2, m) % m;
			p = (p * p) % m;

			if (y % 2 == 0)
				return p;
			else
				return (x * p) % m;
		}

		// Function to return gcd of a and b
		static long gcd(long a, long b) {
			if (a == 0)
				return b;
			return gcd(b % a, a);
		}

		static int highestPowerOf2(int n) {
			return (n & (~(n - 1)));
		}

	}
	// template code

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

	}

}
class Point{
	double x,y;
	public Point(double x,double y) {
		this.x=x;
		this.y=y;
	}
	public double d(Point p2) {
		
		return Math.sqrt(Math.pow(p2.x-this.x, 2)+Math.pow(p2.y-this.y, 2));
	}
	public Point mp(Point p2) {
		return new Point((p2.x+this.x)/2, (p2.y+this.y)/2);
	}
}
class TCS implements Comparable<TCS>, Comparator<TCS> {
	long i1, i2;
	int flag;

	@Override
	public String toString() {
		// TODO Auto-generated method stub
		return "i1:" + i1 + "  i2:" + i2;
	}

	TCS(long i1, long i2) {
		this.i1 = i1;
		this.i2 = i2;
	}

	@Override
	public int compareTo(TCS o) {
		// TODO Auto-generated method stub
		return compare(this, o);
	}

	@Override
	public int compare(TCS o1, TCS o2) {
		// TODO Auto-generated method stub
		return (int) ((o1.i1 == o2.i1) ? o1.i2 - o2.i2 : o1.i1 - o2.i1);
	}

	@Override
	public int hashCode() {
		// TODO Auto-generated method stub
		return super.hashCode();
	}

	@Override
	public boolean equals(Object obj) {
		// TODO Auto-generated method stub
		return super.equals(obj);
	}

}

class Pair implements Comparator<Pair>, Comparable<Pair> {
	int key, value;

	@Override
	public String toString() {
		// TODO Auto-generated method stub
		return "key:" + key + " value: " + value;
	}

	public Pair(int i, int j) {
		key = i;
		value = j;

	}

	@Override
	public int compare(Pair o1, Pair o2) {
		// TODO Auto-generated method stub
		return o1.compareTo(o2);
	}

	@Override
	public int hashCode() {
		// TODO Auto-generated method stub
		return key;
	}

	@Override
	public int compareTo(Pair o) {
		// TODO Auto-generated method stub
		return this.key - o.key;
	}

}