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.awt.geom.Point2D;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;


public class CF274C {

    public static void main(String[] args) throws Exception {
        new CF274C().solve();
    }

    private void solve() throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Point[] ps = new Point[n];
        // boolean[][] bitmap = new boolean[40001][40001];
        // int diff = 2000;
        for (int i = 0; i < n; i++) {
            ps[i] = new Point(sc.nextInt(), sc.nextInt());
            // bitmap[(int)ps[i].y + diff][(int)ps[i].x + diff] = true;
        }
        double maxT = -1;
        for (int i = 0; i < n; i++) {
            Point a = ps[i];
            for (int j = i + 1; j < n; j++) {
                Point b = ps[j];
                Point ab = b.subtract(a);
                mainLoop: for (int k = j + 1; k < n; k++) {
                    Point c = ps[k];
                    Point bc = c.subtract(b);
                    Point ca = a.subtract(c);
                    double abDotBc = ab.dot(bc);
                    double bcDotCa = bc.dot(ca);
                    double caDotAb = ca.dot(ab);
//                    System.out.println(abDotBc);
//                    System.out.println(bcDotCa);
//                    System.out.println(caDotAb);
                    if (abDotBc < 0 && bcDotCa < 0 && caDotAb < 0) {  // 鋭角
                        if (ab.cross(bc) == 0) continue;
                        Point ct = circumcenter(a, b, c);
                        double t = ct.distanceSq(a);
                        if (t < maxT) continue mainLoop;
                        for (int l = 0; l < n; l++) {
                            if (ct.distanceSq(ps[l]) + EPS < t) continue mainLoop;
                        }
                        // System.out.println("!!!" + i + "," + j + "," + k + "," +t);
                        maxT = Math.max(maxT, t);
                    }
                    else if (abDotBc * bcDotCa * caDotAb == 0) {  // 直角
                        Point ref;
                        if (abDotBc == 0) ref = reflection(c, a, b);
                        else if (bcDotCa == 0) ref = reflection(a, b, c);
                        else ref = reflection(b, c, a);
                        double[] dists = new double[] {
                                a.distanceSq(b), a.distanceSq(c), a.distanceSq(ref),
                                b.distanceSq(c), b.distanceSq(ref), c.distanceSq(ref) };
                        Arrays.sort(dists);
//                        System.out.println(Arrays.toString(dists));
                        if (!approxEquals(dists[1], dists[2])) continue;
                        
                        boolean hasThat = false;
                        Point ct = circumcenter(a, b, c);
                        double t = ct.distanceSq(a);
                        if (t < maxT) continue mainLoop;
                        for (int l = 0; l < n; l++) {
                            if (ct.distanceSq(ps[l]) + EPS < t) continue mainLoop;
                            hasThat = hasThat || ref.equals(ps[l]);
                        }
//                         System.out.println("!!!" + i + "," + j + "," + k + hasThat + "," + ref +","+ t);
                        if (hasThat) maxT = Math.max(maxT, t);
                    }
                }
            }
        }
        if (maxT > 0) System.out.printf("%.6f%n", Math.sqrt(maxT));
        else System.out.println(-1);
    }

    static final double EPS = 1e-4;

    static class Point extends Point2D.Double {

        public Point() {
        }

        public Point(double x, double y) {
            super(x, y);
        }

        /** dot(v1,v2)=|v1||v2|cosθ */
        double dot(Point p) {
            return x * p.x + y * p.y;
        }

        /**
         * cross(v1,v2)=|v1||v2|sinθ=
         * |x1 y1|
         * |x2 y2|
         */
        double cross(Point p) {
            return x * p.y - y * p.x;
        }

        double distanceSqr() {
            return x * x + y * y;
        }

        double distance() {
            return Math.sqrt(distanceSqr());
        }

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

        Point multiply(double k) {
            return new Point(k * x, k * y);
        }

        Point multiply(Point p) {
            return new Point(x * p.x - y * p.y, x * p.y + p.x * y);
        }

        Point subtract(Point begin) {
            return new Point(x - begin.x, y - begin.y);
        }

        @Override
        public boolean equals(Object obj) {
            if (this == obj) return true;
            if (obj == null) return false;
            if (getClass() != obj.getClass()) return false;
            Point other = (Point) obj;
            if (!approxEquals(x, other.x)) return false;
            if (!approxEquals(y, other.y)) return false;
            return true;
        }

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

    static final Comparator<Point> XY_COMPARATOR = new Comparator<Point>() {
        @Override
        public int compare(Point o1, Point o2) {
            if (!approxEquals(o1.x, o2.x)) return (int) Math.signum(o1.x - o2.x);
            if (!approxEquals(o1.y, o2.y)) return (int) Math.signum(o1.y - o2.y);
            return 0;
        }

    };

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

    /*
     * @see http://www.prefield.com/algorithm/geometry/distance.html
     */

    static Point projection(Point a1, Point a2, Point p) {
        Point a = a2.subtract(a1);
        p = p.subtract(a1);
        double t = a.dot(p) / a.distanceSqr();
        return a1.add(a.multiply(t));
    }

    static Point reflection(Point a1, Point a2, Point p) {
        Point dir = projection(a1, a2, p).subtract(p);
        return p.add(dir.multiply(2));
    }

    /** @see http://www.deqnotes.net/acmicpc/2d_geometry/lines#intersection_of_lines */
    static Point crosspointLL(Point a1, Point a2, Point b1, Point b2) {

        Point a = a2.subtract(a1);
        Point b = b2.subtract(b1);
        double d1 = b.cross(b1.subtract(a1));
        double d2 = b.cross(a);
        if (Math.abs(d1) < EPS && Math.abs(d2) < EPS) return a1;  // same line
        if (Math.abs(d2) < EPS) throw new IllegalArgumentException(
                "PRECONDITION NOT SATISFIED");
        return a1.add(a.multiply(d1 / d2));
    }

    static Point circumcenter(Point a, Point b, Point c) {
        a = a.subtract(c).multiply(0.5);
        Point an = a.multiply(new Point(0, 1));
        b = b.subtract(c).multiply(0.5);
        Point bn = b.multiply(new Point(0, 1));
        return crosspointLL(a, a.add(an), b, b.add(bn)).add(c);
    }

}