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.FilterInputStream;
import java.io.BufferedInputStream;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */

public class Main {
    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            public void run() {
                new Main().solve();
            }
        }, "1", 1 << 26).start();
    }

    void solve() {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ScanReader in = new ScanReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DNatureReserve solver = new DNatureReserve();
        solver.solve(1, in, out);
        out.close();
    }

    static class DNatureReserve {
        int[][] ar;

        boolean checkit(double val) {
            double minx = -1e9;
            double maxx = 1e9;
            for (int i = 0; i < ar.length; i++) {
                double d = Math.sqrt(2 * val * ar[i][1] - ((double) ar[i][1] * ar[i][1]));
                minx = Math.max(ar[i][0] - d, minx);
                maxx = Math.min(ar[i][0] + d, maxx);
            }
            if (minx <= maxx) return true;
            return false;
        }

        public void solve(int testNumber, ScanReader in, PrintWriter out) {
            int n = in.scanInt();
            ar = new int[n][2];
            boolean less = false;
            boolean more = false;
            for (int i = 0; i < n; i++) {
                ar[i][0] = in.scanInt();
                ar[i][1] = in.scanInt();
                if (ar[i][1] < 0) less = true;
                else if (ar[i][1] > 0) more = true;
                ar[i][1] = Math.abs(ar[i][1]);
            }
            if (less && more) {
                out.println(-1);
                return;
            }
            double low = 0;
            double high = 1e15;
            double ans = -1;
            for (int i = 0; i < 500; i++) {
                double mid = (low + high) / 2;
                if (checkit(mid)) {
                    ans = mid;
                    high = mid - (1e-9);
                } else {
                    low = mid + (1e-9);
                }
            }
            out.println(ans);

        }

    }

    static class ScanReader {
        private byte[] buf = new byte[4 * 1024];
        private int index;
        private BufferedInputStream in;
        private int total;

        public ScanReader(InputStream inputStream) {
            in = new BufferedInputStream(inputStream);
        }

        private int scan() {
            if (index >= total) {
                index = 0;
                try {
                    total = in.read(buf);
                } catch (Exception e) {
                    e.printStackTrace();
                }
                if (total <= 0) return -1;
            }
            return buf[index++];
        }

        public int scanInt() {
            int integer = 0;
            int n = scan();
            while (isWhiteSpace(n)) n = scan();
            int neg = 1;
            if (n == '-') {
                neg = -1;
                n = scan();
            }
            while (!isWhiteSpace(n)) {
                if (n >= '0' && n <= '9') {
                    integer *= 10;
                    integer += n - '0';
                    n = scan();
                }
            }
            return neg * integer;
        }

        private boolean isWhiteSpace(int n) {
            if (n == ' ' || n == '\n' || n == '\r' || n == '\t' || n == -1) return true;
            else return false;
        }

    }
}