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.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;

public class D {
	
	class Point {
		double x, y;
		Point(double a, double b) {
			x = a; y = b;
		}
		double dot(Point p) {
			double nx = p.x * x;
			double ny = p.y * y;
			return nx + ny;
		}
		double mag() {
			return Math.sqrt(x*x + y*y);
		}
		double dist(Point p) {
			double dx = p.x - x, dy = p.y - y;
			return Math.sqrt(dx*dx + dy*dy);
		}
	}
	
	int n;
	Point[] pts;
	
	double check(double xx) {
		double ans = 0;
		for(Point p : pts) {
			double x = p.x - xx;
			double y = p.y;
			double r = (x*x + y*y) / (2 * y);
			ans = Math.max(ans, r);
		}
		return ans;
	}
	
	public void solve(JS in, PrintWriter out) {
		n = in.nextInt();
		pts = new Point[n];
		boolean above = false, below = false;
		for(int i = 0; i < n; ++i) {
			pts[i] = new Point(in.nextInt(), in.nextInt());
			above |= pts[i].y > 0;
			below |= pts[i].y < 0;
		}
		if(above && below) {
			out.println(-1);
			return;
		}
		if(below) for(Point p : pts) p.y = -p.y;
		double lo = -1e7, hi = 1e7;
		for(int i = 0; i < 200; ++i) {
			double shift = (hi - lo) / 3;
			double mid = (lo + hi) / 2;
			double midl = lo + shift;
			double midh = hi - shift;
			
			double lowR = check(midl);
			double r = check(mid);
			double higR = check(midh);
			
			if(lowR > r) lo = midl;
			if(higR > r) hi = midh;
		}
		
		out.println(check(lo));
	}
	
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		new D().solve(in, out);
		out.close();
	}
	
	static class JS {
		public int BS = 1<<16;
		public char NC = (char)0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public JS() {
			in = new BufferedInputStream(System.in, BS);
		}

		public JS(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar(){
			while(bId==size) {
				try {
					size = in.read(buf);
				}catch(Exception e) {
					return NC;
				}
				if(size==-1)return NC;
				bId=0;
			}
			return (char)buf[bId++];
		}

		public int nextInt() {
			return (int)nextLong();
		}

		public long nextLong() {
			num=1;
			boolean neg = false;
			if(c==NC)c=nextChar();
			for(;(c<'0' || c>'9'); c = nextChar()) {
				if(c=='-')neg=true;
			}
			long res = 0;
			for(; c>='0' && c <='9'; c=nextChar()) {
				res = (res<<3)+(res<<1)+c-'0';
				num*=10;
			}
			return neg?-res:res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c!='.' ? cur:cur+nextLong()/num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c>32) {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while(c<=32)c=nextChar();
			while(c!='\n') {
				res.append(c);
				c=nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if(c>32)return true;
			while(true) {
				c=nextChar();
				if(c==NC)return false;
				else if(c>32)return true;
			}
		}
	}
}