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:
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 */
import java.io.*;
import java.util.*;
import java.math.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "" ;
    boolean local = false;
    int inf=0x7FFFFFFF;
    int MOD2=(int)(1e9+7);
    int n;
    int [][]a;
    double calc(double arc){
        double ret=0;
        for(int i=0;i<n;i++){
            double ans=0;
            double a1=(a[i][0]+arc)/2;
            double a2=a[i][1]/2.0;
            double k1=a[i][1]/(a[i][0]-arc);
            double k2=-1/k1;
            ans=a2+(arc-a1)*k2;
            ret=Math.max(ret,ans);
        }
        return ret;
    }
    void solve() {
        n=ni();
        a=new int[n][2];
        boolean up=false,down=false;
        for(int i=0;i<n;i++){
            a[i][0]=ni();
            a[i][1]=ni();
            if(a[i][1]>0)up=true;
            if(a[i][1]<0)down=true;
            a[i][1]=Math.abs(a[i][1]);
        }
        if(up&&down)out.println(-1);
        else{
            double L=-3e7,R=3e7;
            while(Math.abs(R-L)>1e-7){
                double midl=L+(R-L)/3;
                double midr=R-(R-L)/3;
                double ansl=calc(midl);
                double ansr=calc(midr);
                if(ansl>ansr)L=midl;
                else R=midr;
            }
            out.printf("%.7f",calc(L));
        }
    }
    public class Node implements Comparable{
        public int x,y;
        public Node(int x,int y){
            this.x=x;
            this.y=y;
        }
        public int compareTo(Object o) {
            Node to=(Node)o;
            if(this.x>to.x) return 1;
            else if(this.x==to.x) return 0;
            else return -1;
        }
        public void show(){
            out.println(x+" "+y);
        }
    }
    long[] exgcd(long a, long b) {
        if (b == 0) return new long[]{1,0,a};
        long[] res = exgcd(b, a%b);
        long t = res[0]; res[0] = res[1]; res[1] = t;
        res[1] -= a/b*res[0];
        return res;
    }
    long gcd(long a,long b){
        return b==0?a:gcd(b,a%b);
    }
    long lcm(long a,long b){
        return a*b/gcd(a,b);
    }
    private void run() {
        is = local? new ByteArrayInputStream(INPUT.getBytes()):System.in;
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    public static void main(String[] args) throws Exception { new Main().run(); }
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte(){
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    private String ns(){
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    private char[] ns(int n){
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    private char[][] nm(int n, int m){
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    private int[] na(int n){
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    private int ni(){
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private long nl(){
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private void tr(Object... o) { if(local)System.out.println(Arrays.deepToString(o)); }
}