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.BufferedInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.List;
import java.util.StringJoiner;
import java.util.function.IntUnaryOperator;
import java.util.function.LongUnaryOperator;

class Main {
    static In in = new In();
    static Out out = new Out();
    static long mod = 1000000007;
    static long inf = 0xfffffffffffffffL;

    static double EPS = 1e-8;
    void solve() {
        int n = in.nextInt();
        List<Point> list = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            list.add(new Point(in.nextInt(), in.nextInt()));
        }
        Point p = minBall(list, n);
        double ans = 0;
        for (Point point : list) {
            ans = Math.max(ans, norm(point, p));
        }
        out.println(Math.sqrt(ans));
    }

    Point minBall(List<Point> list, int n) {
        Point pos = new Point(0, 0);
        double ratio = 0.5;
        while (ratio > EPS) {
            for (int i = 0; i < 100; i++) {
                double max = -1;
                int id = -1;
                for (int j = 0; j < n; j++) {
                    double d = norm(pos, list.get(j));
                    if (max < d) {
                        max = d;
                        id = j;
                    }
                }
                Point dt = sub(list.get(id), pos);
                pos.x += dt.x * ratio;
                pos.y += dt.y * ratio;
            }
            ratio /= 2;
        }
        return pos;
    }

    double norm(Point a, Point b) {
        return (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
    }

    Point sub(Point a, Point b) {
        return new Point(a.x - b.x, a.y - b.y);
    }

    static class Point {
        double x, y;

        Point(double x, double y) {
            this.x = x;
            this.y = y;
        }
    }

    public static void main(String[]$) {
        new Main().solve();
        out.flush();
    }
}

class In {
    private BufferedInputStream reader = new BufferedInputStream(System.in);
    private byte[] buffer = new byte[0x10000];
    private int i = 0;
    private int length = 0;

    private int read() {
        if (i == length) {
            i = 0;
            try {
                length = reader.read(buffer);
            } catch (IOException ignored) {
            }
            if (length == -1) {
                return -1;
            }
        }
        return buffer[i++];
    }

    String next() {
        StringBuilder builder = new StringBuilder();
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        while ('!' <= b && b <= '~') {
            builder.appendCodePoint(b);
            b = read();
        }
        return builder.toString();
    }

    int nextInt() {
        return (int)nextLong();
    }

    long nextLong() {
        int b = read();
        while (b < '!' || '~' < b) {
            b = read();
        }
        int i = 0;
        if (b == '-') {
            i = 1;
            b = read();
        }
        long n = 0;
        while ('0' <= b && b <= '9') {
            n = n * 10 + b - '0';
            b = read();
        }
        return i == 0 ? n : -n;
    }

    char[][] nextCharArray(int n, int m) {
        char[][] a = new char[n][m];
        for (int i = 0; i < n; i++) {
            a[i] = next().toCharArray();
        }
        return a;
    }

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

    int[] nextIntArray(int n, IntUnaryOperator op) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsInt(nextInt());
        }
        return a;
    }

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

    long[] nextLongArray(int n, LongUnaryOperator op) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = op.applyAsLong(nextLong());
        }
        return a;
    }
}

class Out {
    private static PrintWriter out = new PrintWriter(System.out);

    void println(Object... a) {
        StringJoiner joiner = new StringJoiner(" ");
        for (Object obj : a) {
            joiner.add(String.valueOf(obj));
        }
        out.println(joiner);
    }

    void flush() {
        out.flush();
    }
}