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.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class D {
        Point[] points;
        long MAX = 12345678;
        double DELTA = 1e-7;

        double findRad(double cx) {
            double maxc = 0.0;
            for (int i = 0; i < points.length; i++) {
                double midx = (cx + points[i].x) / 2.0;
                double midy = (points[i].y) / 2.0;
                double px = midx + points[i].y - midy;
                double py = midy + midx - points[i].x;
                Line l = new Line(midx, midy, px, py);
                double c = (-l.a * cx - l.c) / l.b;
                maxc = Math.max(c, maxc);
            }
            return maxc;
        }

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.ni();
            int cntNeg = 0;
            int cntPos = 0;
            int cnt0 = 0;
            long minX = MAX;
            long maxX = -MAX;

            points = new Point[n];
            for (int i = 0; i < n; i++) {
                points[i] = new Point(in.ni(), in.ni());
                minX = Math.min(points[i].x, minX);
                maxX = Math.max(points[i].x, maxX);
                if (points[i].y > 0)
                    cntPos++;
                else if (points[i].y < 0)
                    cntNeg++;
                else
                    cnt0++;
            }
            if (cnt0 > 1 || cntNeg > 0 && cntPos > 0) {
                out.println(-1);
                return;
            }
            if (cntNeg > 0) {
                for (int i = 0; i < n; i++) {
                    points[i].y *= -1;
                }
            }
            long minY = MAX;
            long maxY = -MAX;
            for (int i = 0; i < n; i++) {
                minY = Math.min(points[i].y, minY);
                maxY = Math.max(points[i].y, maxY);
            }
            double l = minX;
            double r = maxX;
            while (r - l > DELTA) {
                double m1 = l + (r - l) / 3.0;
                double m2 = r - (r - l) / 3.0;
                if (findRad(m1) > findRad(m2)) {
                    l = m1;
                } else {
                    r = m2;
                }
            }
            out.printf("%f%n", findRad(l));

        }

        class Point {
            long x;
            long y;

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

        }

        class Line {
            double a;
            double b;
            double c;

            public Line(double px, double py, double qx, double qy) {
                a = py - qy;
                b = qx - px;
                c = -a * px - b * py;
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String ns() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(ns());
        }

    }
}