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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;
 

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyScanner in = new MyScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        F solver = new F();
        solver.solve(1, in, out);
        out.close();
    }
 
    static class F {
        public void solve(int testNumber, MyScanner in, PrintWriter out) {
            int P = in.nextInt();
            int[] x = new int[P];
            int[] y = new int[P];
            for (int i = 0; i < P; i++) {
                x[i] = in.nextInt();
                y[i] = in.nextInt();
            }
 
            double lx = 0, hx = 1e8;
            double ly = 0, hy = 1e8;
            while (hx - lx > 1e-9) {
                double llx = (lx * 2 + hx) / 3;
                double hhx = (lx + hx * 2) / 3;
 
                double lly, hhy;
                double low = 0, hi = 1e8;
                while (hi - low > 1e-9) {
                    double ll = (low * 2 + hi) / 3;
                    double hh = (low + hi * 2) / 3;
                    double temp1 = calc(x, y, llx, ll);
                    double temp2 = calc(x, y, llx, hh);
                    if (temp1 < temp2) {
                        hi = hh;
                    } else {
                        low = ll;
                    }
                }
                lly = hi;
 
                low = 0;
                hi = 1e8;
                while (hi - low > 1e-9) {
                    double ll = (low * 2 + hi) / 3;
                    double hh = (low + hi * 2) / 3;
                    double temp1 = calc(x, y, hhx, ll);
                    double temp2 = calc(x, y, hhx, hh);
                    if (temp1 < temp2) {
                        hi = hh;
                    } else {
                        low = ll;
                    }
                }
                hhy = hi;
 
                double temp1 = calc(x, y, llx, lly);
                double temp2 = calc(x, y, hhx, hhy);
                if (temp1 < temp2) {
                    hx = hhx;
                    hy = hhy;
                } else {
                    lx = llx;
                    ly = lly;
                }
            }
            double ret = calc(x, y, hx, hy);
            out.printf("%.6f\n", ret);
        }
 
        private double calc(int[] x, int[] y, double px, double py) {
            double len = 0;
            for (int i = 0; i < x.length; i++) {
                double temp = Math.sqrt(Math.pow(px - x[i], 2) + Math.pow(py - y[i], 2));
                len = Math.max(len, temp);
            }
            return len;
        }
 
    }
 
    static class MyScanner {
        private BufferedReader in;
        private StringTokenizer st;
 
        public MyScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }
 
        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
 
        public int nextInt() {
            return Integer.parseInt(next());
        }
 
    }
}