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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;
import java.util.Map.Entry;

public class Main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000000 + 7;

	private StringBuilder ans_sb;

	private void soln()
	{
		int n = nextInt();
		int c1 = 0;
		int c2 = 0;
		int c3 = 0;
		double[][] cor = new double[n][2];
		for (int i = 0; i < n; i++) {
			double x = nextInt();
			double y = nextInt();
			if (y == 0)
				c3++;
			else if (y < 0) {
				c1++;
				y = -y;
			} else
				c2++;
			cor[i][0] = x;
			cor[i][1] = y;
		}
		if (c3 >= 2 || (c1 > 0 && c2 > 0))
			pw.println(-1);
		else {
			double l = 0;
			double r = 1e14;
			double ans = -1;
			for (int j = 0; j < 100; j++) {
				double mid = (l + r) / 2;
				double rl = cor[0][0] - Math.sqrt((2 * mid - cor[0][1]) * cor[0][1]);
				double rr = cor[0][0] + Math.sqrt((2 * mid - cor[0][1]) * cor[0][1]);
				for (int i = 1; i < n; i++) {
					double rrl = cor[i][0] - Math.sqrt((2 * mid - cor[i][1]) * cor[i][1]);
					double rrr = cor[i][0] + Math.sqrt((2 * mid - cor[i][1]) * cor[i][1]);
					rl = Math.max(rl, rrl);
					rr = Math.min(rr, rrr);
				}
				if (rl <= rr) {
					ans = mid;
					r = mid - 1;
				} else {
					l = mid + 1;
				}
			}
			pw.println(ans);
		}
	}

	class Centroid
	{
		private int n;
		private LinkedList<Integer>[] tree;
		private int[] sPar;
		private int[] lvl;
		private int[] size;
		private boolean[] v;
		private int nn;

		public Centroid(int a, LinkedList<Integer>[] l)
		{
			n = a;
			tree = l;
			size = new int[n];
			sPar = new int[n];
			lvl = new int[n];
			v = new boolean[n];
			decompose(0, -1);
		}

		private void decompose(int cur, int prev)
		{
			nn = 0;
			dfs(cur, cur);
			Integer centroid = findCentroid(cur, prev);
			if (prev == -1) {
				prev = centroid;
				lvl[centroid] = 0;
			} else {
				lvl[centroid] = lvl[prev] + 1;
			}
			// System.out.println(centroid);
			v[centroid] = true;
			sPar[centroid] = prev;
			Iterator<Integer> it = tree[centroid].listIterator();
			while (it.hasNext()) {
				int x = it.next();
				// tree[x].remove(centroid);
				if (!v[x])
					decompose(x, centroid);
				// tree[x].add(0,centroid);
			}
			tree[centroid].clear();
		}

		private void dfs(int cur, int prev)
		{
			// System.out.println(cur);
			size[cur] = 1;
			nn++;
			Iterator<Integer> it = tree[cur].listIterator();
			while (it.hasNext()) {
				int x = it.next();
				if (x != prev && !v[x]) {
					dfs(x, cur);
					size[cur] += size[x];
				}
			}
		}

		private int findCentroid(int cur, int prev)
		{
			Iterator<Integer> it = tree[cur].listIterator();
			while (it.hasNext()) {
				int x = it.next();
				if (x != prev && size[x] > nn / 2 && !v[x]) {
					return findCentroid(x, cur);
				}
			}
			return cur;
		}

		private int[] retPar()
		{
			return sPar;
		}

		private int[] retLvl()
		{
			return lvl;
		}
	}

	private String solveEqn(long a, long b)
	{
		long x = 0, y = 1, lastx = 1, lasty = 0, temp;
		while (b != 0) {
			long q = a / b;
			long r = a % b;
			a = b;
			b = r;
			temp = x;
			x = lastx - q * x;
			lastx = temp;
			temp = y;
			y = lasty - q * y;
			lasty = temp;
		}
		return lastx + " " + lasty;
	}

	private static void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}

	private long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}

	private long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}

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

	public StringBuilder solve()
	{
		InputReader(System.in);
		/*
		 * try { InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		 * } catch(FileNotFoundException e) {}
		 */
		pw = new PrintWriter(System.out);
		// ans_sb = new StringBuilder();
		soln();

		pw.close();
		// System.out.println(ans_sb);
		return ans_sb;
	}

	public void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

	private boolean isWhitespace(int c)
	{
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private boolean isEndOfLine(int c)
	{
		return c == '\n' || c == '\r' || c == -1;
	}

	private int read()
	{
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private int nextInt()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private long nextLong()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private String nextLine()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private int[] nextIntArray(int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++) {
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}