Problem: There is a forest that we model as a plane and live n rare animals. Animal number i has its lair in the point (x_{i}, y_{i}). In order to protect them, a decision to build a nature reserve has been made.

The reserve must have a form of a circle containing all lairs. There is also a straight river flowing through the forest. All animals drink from this river, therefore it must have at least one common point with the reserve. On the other hand, ships constantly sail along the river, so the reserve must not have more than one common point with the river.

For convenience, scientists have made a transformation of coordinates so that the river is defined by y = 0. Check whether it is possible to build a reserve, and if possible, find the minimum possible radius of such a reserve.

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — the number of animals. 

Each of the next n lines contains two integers x_{i}, y_{i} (-10^7 ≤ x_{i}, y_{i} ≤ 10^7) — the coordinates of the i-th animal's lair. It is guaranteed that y_{i} ≠ 0. No two lairs coincide.

Output

If the reserve cannot be built, print -1. Otherwise print the minimum radius. Your answer will be accepted if absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.

Examples

Input

1
0 1


Output

0.5

Input

3
0 1
0 2
0 -3


Output

-1


Input

2
0 1
1 1


Output

0.625

Note

In the first sample it is optimal to build the reserve with the radius equal to 0.5 and the center in (0,\ 0.5).

In the second sample it is impossible to build a reserve.

In the third sample it is optimal to build the reserve with the radius equal to 5/8 and the center in (1/2,\ 5/8).

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.io.InputStream;

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

    static class TaskD {
        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.nextInt();
            Point[] p = in.readPolygon(n);

            int maxY = p[0].y;
            int minY = p[0].y;

            for (Point pi : p) {
                maxY = Math.max(pi.y, maxY);
                minY = Math.min(pi.y, minY);
            }

            if (maxY > 0 && minY < 0) {
                out.println(-1);
                return;
            }
            if (p[0].y < 0) for (Point pi : p) pi.y = -pi.y;

            if (n == 1) {
                out.println(p[0].y / 2D);
                return;
            }

            double low = 0D;
            double high = 5e14;
            for (int i = 0; i < 200; ++i) {
                double r = (high + low) / 2;
                if (check(p, r)) high = r;
                else low = r;
            }

            out.printf("%.12f", (high + low) / 2);
        }

        private boolean check(Point[] p, double r) {
            double left = Double.NEGATIVE_INFINITY;
            double right = Double.POSITIVE_INFINITY;
            for (Point pi : p) {
                if (pi.y > 2 * r) return false;

//            double k = Math.sqrt(Math.abs(pi.y * pi.y -2 * r * pi.y));
                double k = Math.sqrt(pi.y) * Math.sqrt(Math.abs(2 * r - pi.y)); //   Math.abs(pi.y * pi.y -2 * r * pi.y));
                left = Math.max(left, pi.x - k);
                right = Math.min(right, pi.x + k);
            }

            return left <= right + 1e-12;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void close() {
            super.close();
        }

    }

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

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


        public boolean equals(Object that) {
            Point other = (Point) that;
            return this.x == other.x && this.y == other.y;
        }


        public int compareTo(Point o) {
            if (x != o.x) return Integer.compare(x, o.x);
            return Integer.compare(y, o.y);
        }


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


        public int hashCode() {
            return 31 * x + y;
        }

        public Point clone() {
            return new Point(this.x, this.y);
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

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

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

        public Point[] readPolygon(int n) {
            Point[] vertex = new Point[n];
            for (int i = 0; i < n; ++i)
                vertex[i] = new Point(nextInt(), nextInt());

            return vertex;
        }

    }
}