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.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.math.BigInteger;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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();
	}
}

class TaskC {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        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 = -1.0;
        long[][] a = new long[n][n];
        long[][] b = new long[n][n];
        long[][] c = new long[n][n];
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j) {
                if (i == j) continue;
                a[i][j] = 2 * (x[j] - x[i]);
                b[i][j] = 2 * (y[j] - y[i]);
                c[i][j] = x[i] * x[i] + y[i] * y[i] - x[j] * x[j] - y[j] * y[j];
            }
        for (int i = 0; i < n; ++i)
            for (int j = i + 1; j < n; ++j) {
                for (int k = j + 1; k < n; ++k) {
                    long x1 = x[i];
                    long y1 = y[i];
                    long x2 = x[j];
                    long y2 = y[j];
                    long x3 = x[k];
                    long y3 = y[k];
                    if ((x2 - x1) * (x3 - x1) + (y2 - y1) * (y3 - y1) <= 0) continue;
                    if ((x3 - x2) * (x1 - x2) + (y3 - y2) * (y1 - y2) <= 0) continue;
                    if ((x1 - x3) * (x2 - x3) + (y1 - y3) * (y2 - y3) <= 0) continue;
                    res = updateRes(n, x, y, res, a, b, c, i, j, k, x1, y1);
                }
                {
                    long d = (x[i] - x[j]) * (x[i] - x[j]) + (y[i] - y[j]) * (y[i] - y[j]);
                    long sx = x[i] + x[j];
                    long sy = y[i] + y[j];
                    long dx = x[j] - x[i];
                    long dy = y[j] - y[i];
                    boolean any = false;
                    int anyK = -1;
                    outer: for (int k = 0; k < n; ++k)
                        for (int t = k + 1; t < n; ++t) {
                            long nd = (x[k] - x[t]) * (x[k] - x[t]) + (y[k] - y[t]) * (y[k] - y[t]);
                            long nsx = x[k] + x[t];
                            long nsy = y[k] + y[t];
                            long ndx = x[t] - x[k];
                            long ndy = y[t] - y[k];
                            if (d == nd && sx == nsx && sy == nsy && dx * ndy - dy * ndx != 0) {
                                any = true;
                                anyK = k;
                                break outer;
                            }
                        }
                    if (any) res = updateRes(n, x, y, res, a, b, c, i, j, anyK, x[i], y[i]);
                }
            }
        out.printf("%.10f\n", res);
    }

    private double updateRes(int n, int[] x, int[] y, double res, long[][] a, long[][] b, long[][] c, int i, int j, int k, long x1, long y1) {
        long a1 = a[i][j];
        long a2 = a[j][k];
        long b1 = b[i][j];
        long b2 = b[j][k];
        long c1 = c[i][j];
        long c2 = c[j][k];
        long z = a1 * b2 - a2 * b1;
        if (z == 0) return res;
        long px = -(c1 * b2 - c2 * b1);
        long py = -(a1 * c2 - a2 * c1);
        BigInteger d = BigInteger.valueOf(px - z * x1).pow(2).add(BigInteger.valueOf(py - z * y1).pow(2));
        boolean ok = true;
        for (int t = 0; t < n; ++t) {
            BigInteger dd = BigInteger.valueOf(px - z * x[t]).pow(2).add(BigInteger.valueOf(py - z * y[t]).pow(2));
            if (dd.compareTo(d) < 0) {
                ok = false;
                break;
            }
        }
        if (ok) {
            res = Math.max(res, Math.sqrt(d.doubleValue()) / Math.abs(z));
        }
        return res;
    }
}

class InputReader {
    public BufferedReader reader;
    public StringTokenizer tokenizer;

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

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

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

    }