Problem: Recently the construction of Berland collider has been completed. Collider can be represented as a long narrow tunnel that contains n particles. We associate with collider 1-dimensional coordinate system, going from left to right. For each particle we know its coordinate and velocity at the moment of start of the collider. The velocities of the particles don't change after the launch of the collider. Berland scientists think that the big bang will happen at the first collision of particles, whose velocities differs in directions. Help them to determine how much time elapses after the launch of the collider before the big bang happens.

Input

The first line contains single integer n (1 ≤ n ≤ 5·105) — amount of particles in the collider. Next n lines contain description of particles. Each particle is described by two integers xi, vi ( - 109 ≤ xi, vi ≤ 109, vi ≠ 0) — coordinate and velocity respectively. All the coordinates are distinct. The particles are listed in order of increasing of coordinates. All the coordinates are in meters, and all the velocities — in meters per second. The negative velocity means that after the start of collider the particle will move to the left, and the positive — that the particle will move to the right.

Output

If there will be no big bang, output -1. Otherwise output one number — how much time in seconds elapses after the launch of the collider before the big bang happens. Your answer must have a relative or absolute error less than 10 - 9.

Examples

Input

3
-5 9
0 1
5 -1


Output

1.00000000000000000000


Input

6
1 3
2 3
3 3
4 -3
5 -1
6 -100


Output

0.02912621359223301065

Solution (in JAVA):

Solution:
import java.io.*;

import java.awt.geom.Point2D;
import java.text.*;
import java.math.*;
import java.util.*;

public class Main implements Runnable {

	final String filename = "";
	final double eps = 5e-10;

	double[] x, v;

	double test(int left, int right) {
		if (v[left] < 0 || v[right - 1] > 0)
			return -1.0;
		double min = 0.0;
		double max = (x[right - 1] - x[left]) / (-v[right - 1] + v[left]);
		for (int j = 0; j < 50 && (max - min) > eps; j++) {
			double mid = (min + max) / 2.0;
			double m1 = x[left] + v[left] * mid;
			double m2 = x[right - 1] + v[right - 1] * mid;
			for (int i = left + 1; i < right - 1; i++) {
				double xx = x[i] + v[i] * mid;
				if (v[i] > 0)
					m1 = Math.max(m1, xx);
				else
					m2 = Math.min(m2, xx);
			}
			if (m1 < m2)
				min = mid;
			else
				max = mid;
		}
		return (min + max) / 2.0;
	}

	public void solve() throws Exception {
		int n = iread();
		x = new double[n];
		v = new double[n];
		for (int i = 0; i < n; i++) {
			x[i] = dread();
			v[i] = dread();
		}

		double time = -1.0;
		int left = 0;
		boolean wasNeg = false;
		for (int i = 0; i < n; i++) {
			if (v[i] < 0)
				wasNeg = true;
			else if (wasNeg) {
				double r = test(left, i);
				if (r > 0.0) {
					if (time < 0.0 || time > r)
						time = r;
				}
				wasNeg = false;
				left = i;
			}
		}
		if (wasNeg) {
			double r = test(left, n);
			if (r > 0.0) {
				if (time < 0.0 || time > r)
					time = r;
			}
		}
		DecimalFormat df = new DecimalFormat("0.0000000000");
		out.write(df.format(time) + "\n");
	}

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new BufferedWriter(new OutputStreamWriter(System.out));
			// in = new BufferedReader(new FileReader(filename + ".in"));
			// out = new BufferedWriter(new FileWriter(filename + ".out"));
			solve();
			out.flush();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	public int iread() throws Exception {
		return Integer.parseInt(readword());
	}

	public double dread() throws Exception {
		return Double.parseDouble(readword());
	}

	public long lread() throws Exception {
		return Long.parseLong(readword());
	}

	BufferedReader in;

	BufferedWriter out;

	public String readword() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) {
		try {
			Locale.setDefault(Locale.US);
		} catch (Exception e) {

		}
		new Thread(new Main()).start();
		// new Thread(null, new Main(), "1", 1<<25).start();
	}
}