Problem: 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}.

Examples

Input

2
0 0
1 0


Output

0.500000000000000000


Input

3
0 0
0 1
1 0


Output

0.707106781186497524


Input

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


Output

6.726812023536805158

Solution (in JAVA):

Solution:
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;

public class Main {
    InputStream is;

    int __t__ = 1;
    int __f__ = 0;
    int __FILE_DEBUG_FLAG__ = __f__;
    String __DEBUG_FILE_NAME__ = "src/E3";

    FastScanner in;
    PrintWriter out;

    public void solve() {
        int n = in.nextInt();
        int[] x = new int[n];
        int[] y = new int[n];
        for (int i = 0; i < n; i++) {
            x[i] = in.nextInt();
            y[i] = in.nextInt();
        }
        double res = 1 << 30;
        for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) {
            double cx = (x[i] + x[j]) / 2.0;
            double cy = (y[i] + y[j]) / 2.0;
            double d = dist2(x[i], y[i], cx, cy);
            if (can(cx, cy, x, y, d)) {
                // System.out.println("(" + x[i] + ", " + y[i] + "), (" + x[j] + ", " + y[j] + ")");
                // System.out.println(cx + " " + cy + " " + d);
                res = Math.min(res, d);
            }
        }
        for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) for (int k = j + 1; k < n; k++) {
            int x1 = x[i], x2 = x[j], x3 = x[k];
            int y1 = y[i], y2 = y[j], y3 = y[k];
            if ((x2 - x1) * (y3 - y2) == (x3 - x2) * (y2 - y1)) {
                continue;
            }
            double xa = (x1 * x1 + y1 * y1) * (y2 - y3)
                    + (x2 * x2 + y2 * y2) * (y3 - y1)
                    + (x3 * x3 + y3 * y3) * (y1 - y2);
            double ya = (x1 * x1 + y1 * y1) * (x3 - x2)
                    + (x2 * x2 + y2 * y2) * (x1 - x3)
                    + (x3 * x3 + y3 * y3) * (x2 - x1);
            double bb = 2.0 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
            double cx = xa / bb;
            double cy = ya / bb;

            double d = dist2(x[i], y[i], cx, cy);
            if (can(cx, cy, x, y, d)) {
                // System.out.println("(" + x1 + ", " + y1 + "), (" + x2 + ", " + y2 + "), (" + x3 + ", " + y3 + ")");
                // System.out.println(cx + " " + cy + " " + d);
                res = Math.min(res, d);
            }

        }
        System.out.println(Math.sqrt(res));
    }

    private boolean can(double cx, double cy, int[] x, int[] y, double d) {
        int n = x.length;
        for (int i = 0; i < n; i++) {
            double nd = dist2(x[i], y[i], cx, cy);
            // System.out.println(i + " " + d + " " + nd);
            if (d - nd < -1e-9) {
                return false;
            }
        }
        return true;
    }

    private double dist(double x1, double y1, double x2, double y2) {
        return Math.sqrt(dist2(x1, y1, x2, y2));
    }

    private double dist2(double x1, double y1, double x2, double y2) {
        double dx = x1 - x2;
        double dy = y1 - y2;
        return dx * dx + dy * dy;
    }

    /* MOD_CALCULATION */
    static long MOD = 1000000007L;
    static long ADD(long a, long b) {
        return (a + b) % MOD;
    }

    static long SUB(long a, long b) {
        return (a - b + MOD) % MOD;
    }

    static long MULT(long a, long b) {
        return (a * b) % MOD;
    }

    static long POW(long a, long x) {
        long res = 1;
        for ( ; x > 0; x >>= 1) {
            if (x % 2 == 1) res = MULT(res, a);
            a = MULT(a, a);
        }

        return res;
    }

    static long DIV(long a, long b) {
        return MULT(a, POW(b, MOD - 2));
    }
    /* end */

    public void run() {
        if (__FILE_DEBUG_FLAG__ == __t__) {
            try {
                is = new FileInputStream(__DEBUG_FILE_NAME__);
            } catch (FileNotFoundException e) {
                // TODO 自動生成された catch ブロック
                e.printStackTrace();
            }
            System.out.println("FILE_INPUT!");
        } else {
            is = System.in;
        }
        in = new FastScanner(is);
        out = new PrintWriter(System.out);

        solve();
    }

    public static void main(final String[] args) {
        new Main().run();
    }

    class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
            // stream = new FileInputStream(new File("dec.in"));

        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

        int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++)
                array[i] = nextInt();

            return array;
        }

        int[][] nextIntMap(int n, int m) {
            int[][] map = new int[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextIntArray(m);
            }
            return map;
        }

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

        long[] nextLongArray(int n) {
            long[] array = new long[n];
            for (int i = 0; i < n; i++)
                array[i] = nextLong();

            return array;
        }

        long[][] nextLongMap(int n, int m) {
            long[][] map = new long[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextLongArray(m);
            }
            return map;
        }

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

        double[] nextDoubleArray(int n) {
            double[] array = new double[n];
            for (int i = 0; i < n; i++)
                array[i] = nextDouble();

            return array;
        }

        double[][] nextDoubleMap(int n, int m) {
            double[][] map = new double[n][m];
            for (int i = 0; i < n; i++) {
                map[i] = in.nextDoubleArray(m);
            }
            return map;
        }

        String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        String[] nextStringArray(int n) {
            String[] array = new String[n];
            for (int i = 0; i < n; i++)
                array[i] = next();

            return array;
        }

        String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}