Problem: Luyi has n circles on the plane. The i-th circle is centered at (xi, yi). At the time zero circles start to grow simultaneously. In other words, the radius of each circle at time t (t > 0) is equal to t. The circles are drawn as black discs on an infinite white plane. So at each moment the plane consists of several black and white regions. Note that the circles may overlap while growing.

<image>

We define a hole as a closed, connected white region. For instance, the figure contains two holes shown by red border. During growing some holes may be created and it is easy to see that each created hole will disappear eventually. Luyi asks you to find moment of time such that the last hole disappears. In other words, you should find the first moment such that no hole can be seen after that.

Input

The first line of the input contains integer n (1 ≤ n ≤ 100). Each of the next n lines contains two integers xi and yi ( - 104 ≤ xi, yi ≤ 104), indicating the location of i-th circle.

It's guaranteed that no two circles are centered at the same point.

Output

Print the moment where the last hole disappears. If there exists no moment in which we can find holes print -1.

The answer will be considered correct if the absolute or relative error does not exceed 10 - 4.

Examples

Input

3
0 0
1 1
2 2


Output

-1


Input

4
0 0
0 2
2 2
2 0


Output

1.414214


Input

4
0 1
0 -1
-2 0
4 0


Output

2.125000

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.util.List;
import java.util.StringTokenizer;
import java.io.InputStreamReader;
import java.io.IOException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author AlexFetisov
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        private Point[] p;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            p = new Point[n];
            for (int i = 0; i < n; ++i) {
                p[i] = new Point(in);
            }
            double res = -1;
            for (int i = 0; i < n; ++i) {
                for (int j = i + 1; j < n; ++j) {
                    double t = testSquare(i, j);
                    if (t < 1e99) {
                        res = Math.max(res, t);
                    }
                    for (int k = j + 1; k < n; ++k) {
                        t = testTriangle(i, j, k);
                        if (t < 1e99) {
                            res = Math.max(res, t);
                        }
                    }
                }
            }
            if (DoubleUtils.compareTo(res, 0) <= 0) {
                out.println(-1);
                return;
            }
            out.println(res);
        }

        private double testSquare(int i, int j) {
            Point P = p[i].add(p[j]).div(2);
            Line pLine = new Line(p[i], p[j]).perpendicular(P);
            double needDst = P.distanceTo(p[i]);
            List<Point> forSquare = new ArrayList<Point>(2);
            for (Point A : p) {
                if (pLine.contains(A) && DoubleUtils.compareTo(A.distanceTo(P), needDst) == 0) {
                    forSquare.add(A);
                }
            }
            if (forSquare.size() != 2) return 1e100;
            double res = needDst;
            for (Point pp : p) {
                if (DoubleUtils.compareTo(res, pp.distanceTo(P)) > 0) {
                    return 1e100;
                }
            }
            return res;
        }

        private double testTriangle(int i, int j, int k) {
            if (DoubleUtils.compareTo(p[j].sub(p[i]).dotProduct(p[k].sub(p[i])), 0) <= 0 ||
                    DoubleUtils.compareTo(p[i].sub(p[j]).dotProduct(p[k].sub(p[j])), 0) <= 0 ||
                    DoubleUtils.compareTo(p[j].sub(p[k]).dotProduct(p[i].sub(p[k])), 0) <= 0) {
                return 1e100;
            }
            Line l = new Line(p[i], p[j]).perpendicular(p[i].add(p[j]).div(2));
            Line l2 = new Line(p[i], p[k]).perpendicular(p[i].add(p[k]).div(2));
            Point P = l.intersect(l2);
            double res = p[i].distanceTo(P);
            for (Point pp : p) {
                if (DoubleUtils.compareTo(res, pp.distanceTo(P)) > 0) {
                    return 1e100;
                }
            }
            return res;
        }

    }

    static class InputReader {
        private BufferedReader reader;
        private StringTokenizer stt;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                return null;
            }
        }

        public String nextString() {
            while (stt == null || !stt.hasMoreTokens()) {
                stt = new StringTokenizer(nextLine());
            }
            return stt.nextToken();
        }

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

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

    }

    static class Point implements Comparable<Point> {
        public double x;
        public double y;

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

        public Point() {
            this.x = 0;
            this.y = 0;
        }

        public Point(InputReader in) {
            this.x = in.nextDouble();
            this.y = in.nextDouble();
        }


        public String toString() {
            return "(" + x + ", " + y + " )";
        }


        public boolean equals(Object o) {
            Point p = (Point) o;
            return DoubleUtils.compareTo(x, p.x) == 0 && DoubleUtils.compareTo(y, p.y) == 0;
        }


        public int hashCode() {
            int result;
            long temp;
            temp = x != +0.0d ? Double.doubleToLongBits(x) : 0L;
            result = (int) (temp ^ (temp >>> 32));
            temp = y != +0.0d ? Double.doubleToLongBits(y) : 0L;
            result = 31 * result + (int) (temp ^ (temp >>> 32));
            return result;
        }

        public Point add(Point p) {
            return new Point(x + p.x, y + p.y);
        }

        public Point sub(Point p) {
            return new Point(x - p.x, y - p.y);
        }

        public Point div(double k) {
            return new Point(x / k, y / k);
        }

        public double dotProduct(Point p) {
            return x * p.x + y * p.y;
        }

        public double length() {
            return DoubleUtils.sqrt(dotProduct(this));
        }

        public double distanceTo(Point p) {
            return sub(p).length();
        }


        public int compareTo(Point o) {
            int temp = DoubleUtils.compareTo(x, o.x);
            if (temp == 0) {
                return DoubleUtils.compareTo(y, o.y);
            }
            return temp;
        }

    }

    static class DoubleUtils {
        public static final double EPS = 1e-9;

        public static double sqr(double x) {
            return x * x;
        }

        public static int compareTo(double a, double b) {
            if (doubleEqual(a, b)) {
                return 0;
            }
            if (a < b) {
                return -1;
            }
            return 1;
        }

        private static boolean doubleEqual(double a, double b) {
            return Math.abs(a - b) < EPS;
        }

        public static double sqrt(double a) {
            if (compareTo(a, 0) < 0) {
                System.exit(1);
            }
            if (a < 0) return 0;
            return Math.sqrt(a);
        }

        public static double hypot(double a, double b) {
            return sqrt(sqr(a) + sqr(b));
        }

    }

    static class Line {
        public final double a;
        public final double b;
        public final double c;
        public Point p1;
        public Point p2;
        boolean hasPoints;

        public Line(Point p, double angle) {
            a = Math.sin(angle);
            b = -Math.cos(angle);
            c = -p.x * a - p.y * b;
            p1 = p2 = null;
            hasPoints = false;
        }

        public Line(double a, double b, double c) {
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = false;
        }

        public Line(Point p1, Point p2) {
            double a = p2.y - p1.y;
            double b = p1.x - p2.x;
            double c = -(p1.x * a + p1.y * b);
            double h = DoubleUtils.hypot(a, b);
            this.a = a / h;
            this.b = b / h;
            this.c = c / h;
            hasPoints = true;
        }

        public Point intersect(Line other) {
            if (parallel(other)) {
                return null;
            }
            double determinant = b * other.a - a * other.b;
            double x = (c * other.b - b * other.c) / determinant;
            double y = (a * other.c - c * other.a) / determinant;
            return new Point(x, y);
        }

        public boolean parallel(Line other) {
            return DoubleUtils.compareTo(Math.abs(a * other.b - b * other.a), 0) == 0;
        }

        public boolean contains(Point point) {
            return DoubleUtils.compareTo(Math.abs(value(point)), 0) == 0;
        }

        public Line perpendicular(Point point) {
            return new Line(-b, a, b * point.x - a * point.y);
        }

        public double value(Point point) {
            return a * point.x + b * point.y + c;
        }


        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Line line = (Line) o;

            if (!parallel(line)) return false;
            if (Math.abs(a * line.c - c * line.a) > DoubleUtils.EPS || Math.abs(b * line.c - c * line.b) > DoubleUtils.EPS)
                return false;

            return true;
        }

    }
}