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 static java.lang.Math.*;
import static java.lang.System.currentTimeMillis;
import static java.lang.System.exit;
import static java.lang.System.arraycopy;
import static java.util.Arrays.sort;
import static java.util.Arrays.binarySearch;
import static java.util.Arrays.fill;
import java.util.*;
import java.io.*;

public class Main {

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

    BufferedReader in;
    PrintWriter out;
    StringTokenizer st = new StringTokenizer("");

    final int maxn = 111;
    final double eps = 0.000000001;

    int n;
    Point points[] = new Point[maxn];
    double ans = -1;

    double rotate(Point a, Point b, Point c) {
        double x1 = b.x - a.x;
        double y1 = b.y - a.y;
        double x2 = c.x - b.x;
        double y2 = c.y - b.y;
        return x1 * y2 - x2 * y1;
    }

    double fabs(double a) {
        if (a < 0)
            return -a;
        return a;
    }

    boolean inLine(Point a, Point b, Point c) {
        return fabs(rotate(a, b, c)) < eps;
    }

    int sg(double x) {
        if (fabs(x) < eps)
            return 0;
        if (x < 0)
            return -1;
        return 1;
    }

    boolean pointInTreangle(Point p, Point a, Point b, Point c) {
        int sg1 = sg(rotate(p, a, b));
        int sg2 = sg(rotate(p, b, c));
        int sg3 = sg(rotate(p, c, a));
        // System.err.println(rotate(p, a, b));
        // System.err.println(rotate(p, b, c));
        // System.err.println(rotate(p, c, a));
        // System.err.println(sg1+" "+sg2+" "+sg3);
        return sg1 == sg2 && sg1 == sg3 && sg1 != 0;
    }

    Point getCenter(Point a, Point b, Point c) {
        double x1 = a.x;
        double x2 = b.x;
        double x3 = c.x;
        double y1 = a.y;
        double y2 = b.y;
        double y3 = c.y;
        double y = ((y3 * y3 - y2 * y2 + x3 * x3 - x2 * x2) * (x1 - x2) + (y1 * y1 - y2 * y2 + x1 * x1 - x2 * x2) * (x2 - x3)) / (2 * (y2 - y1) * (x3 - x2) + 2 * (y2 - y3) * (x2 - x1));
        double x = ((x3 * x3 - x2 * x2 + y3 * y3 - y2 * y2) * (y1 - y2) + (x1 * x1 - x2 * x2 + y1 * y1 - y2 * y2) * (y2 - y3)) / (2 * (x2 - x1) * (y3 - y2) + 2 * (x2 - x3) * (y2 - y1));
        return new Point(x, y);
    }

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

    void solveInTreangle(Point center, double d) {
        boolean isAns = true;
        for (int i = 0; i < n && isAns; i++)
            isAns = dist(center, points[i]) >= d - eps;
        // System.err.println(d);
        if (isAns)
            ans = max(ans, d);
    }

    void solveInEdge(Point center, Point a, Point b, Point c) {
        int isAns = -1;
        double d = dist(center, a);
        for (int i = 0; i < n && isAns != 0; i++) {
            if (dist(center, points[i]) <= d - eps)
                isAns = 0;
            if (sg(rotate(a, b, c)) * sg(rotate(a, b, points[i])) < 0) {
                if (fabs(dist(center, points[i]) - d) <= eps && isAns != 0)
                    isAns = 1;
            }
        }
        if (isAns == 1)
            ans = max(ans, d);
    }

    private void run() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));// new
                                                                    // FileReader("input.txt"));
        out = new PrintWriter(System.out);// "output.txt");

        n = nextInt();
        for (int i = 0; i < n; i++)
            points[i] = new Point(nextDouble(), nextDouble());

        for (int i = 0; i < n; i++)
            for (int j = i + 1; j < n; j++)
                for (int k = j + 1; k < n; k++)
                    if (!inLine(points[i], points[j], points[k])) {
                        Point p1 = points[i];
                        Point p2 = points[j];
                        Point p3 = points[k];
                        Point center = getCenter(p1, p2, p3);
                        if (pointInTreangle(center, p1, p2, p3)) {

                            solveInTreangle(center, dist(center, p1));
                        } else {
                            if (inLine(center, p1, p2))
                                solveInEdge(center, p1, p2, p3);
                            if (inLine(center, p2, p3))
                                solveInEdge(center, p2, p3, p1);
                            if (inLine(center, p1, p3))
                                solveInEdge(center, p1, p3, p2);
                        }
                    }

        out.println(ans);

        in.close();
        out.close();
    }

    public class Point {
        public double x, y;

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

    void chk(boolean b) {
        if (b)
            return;
        System.out.println(new Error().getStackTrace()[1]);
        exit(999);
    }

    void deb(String fmt, Object... args) {
        System.out.printf(Locale.US, fmt + "%n", args);
    }

    String nextToken() throws IOException {
        while (!st.hasMoreTokens())
            st = new StringTokenizer(in.readLine());
        return st.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    String nextLine() throws IOException {
        st = new StringTokenizer("");
        return in.readLine();
    }

    boolean EOF() throws IOException {
        while (!st.hasMoreTokens()) {
            String s = in.readLine();
            if (s == null)
                return true;
            st = new StringTokenizer(s);
        }
        return false;
    }
}