Problem: The main road in Bytecity is a straight line from south to north. Conveniently, there are coordinates measured in meters from the southernmost building in north direction.

At some points on the road there are n friends, and i-th of them is standing at the point xi meters and can move with any speed no greater than vi meters per second in any of the two directions along the road: south or north.

You are to compute the minimum time needed to gather all the n friends at some point on the road. Note that the point they meet at doesn't need to have integer coordinate. 

Input

The first line contains single integer n (2 ≤ n ≤ 60 000) — the number of friends.

The second line contains n integers x1, x2, ..., xn (1 ≤ xi ≤ 109) — the current coordinates of the friends, in meters.

The third line contains n integers v1, v2, ..., vn (1 ≤ vi ≤ 109) — the maximum speeds of the friends, in meters per second.

Output

Print the minimum time (in seconds) needed for all the n friends to meet at some point on the road. 

Your answer will be considered correct, if its absolute or relative error isn't greater than 10 - 6. Formally, let your answer be a, while jury's answer be b. Your answer will be considered correct if <image> holds.

Examples

Input

3
7 1 3
1 2 1


Output

2.000000000000


Input

4
5 10 3 2
2 3 2 4


Output

1.400000000000

Note

In the first sample, all friends can gather at the point 5 within 2 seconds. In order to achieve this, the first friend should go south all the time at his maximum speed, while the second and the third friends should go north at their maximum speeds.

Solution (in JAVA):

Solution:
/*
 * 
 * @Author  Ajudiya_13(Bhargav Girdharbhai Ajudiya)
 * Dhirubhai Ambani Institute of Information And Communication Technology 
 * 
 */


import java.util.*;
import java.io.*;
import java.lang.*;

public class Code180
{
	
	
	static class InputReader {
		 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;
 
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
 
		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
 
		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));
			return res * sgn;
		}
 
		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}
 
		public String readString() {
			int c = snext();
			while (isSpaceChar(c)) {
				c = snext();
			}
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}
 
		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}
 
		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
 
		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
 
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	
	public static long mod = 1000000007;
	public static int d;
	public static int p;
	public static int q;
	
	public static int[] suffle(int[] a,Random gen)
	{
		int n = a.length;
		for(int i=0;i<n;i++)
		{
			int ind = gen.nextInt(n-i)+i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}
		return a;
	}
	
	public static void swap(int a, int b){
		int temp = a;
		a = b;
		b = temp;
	}
	
	public static ArrayList<Integer> primeFactorization(int n)
	{
		ArrayList<Integer> a =new ArrayList<Integer>();
		for(int i=2;i*i<=n;i++)
		{
			while(n%i==0)
			{
				a.add(i);
				n/=i;
			}
		}
		if(n!=1)
			a.add(n);
		return a;
	}
	
	public static void sieve(boolean[] isPrime,int n)
	{
		for(int i=1;i<n;i++)
			isPrime[i] = true;
		
		isPrime[0] = false;
		isPrime[1] = false;
		
		for(int i=2;i*i<n;i++)
		{
			if(isPrime[i] == true)
			{
				for(int j=(2*i);j<n;j+=i)
					isPrime[j] = false;
			}
		}
	}
	
	public static int GCD(int a,int b)
	{
		if(b==0)
			return a;
		else
			return GCD(b,a%b);
	}
	
	public static long GCD(long a,long b)
	{
		if(b==0)
			return a;
		else
			return GCD(b,a%b);
	}
	
	public static void extendedEuclid(int A,int B)
	{
		if(B==0)
		{
			d = A;
			p = 1 ;
			q = 0;
		}
		else
		{
			extendedEuclid(B, A%B);
			int temp = p;
			p = q;
			q = temp - (A/B)*q;
		}
	}
	
	public static long LCM(long a,long b)
	{
		return (a*b)/GCD(a,b);
	}
	
	public static int LCM(int a,int b)
	{
		return (a*b)/GCD(a,b);
	}
	
	public static int binaryExponentiation(int x,int n)
	{
	    int result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=result * x;
	        x=x*x;
	        n=n/2;
	    }
	    return result;
	}
	
	public static long binaryExponentiation(long x,long n)
	{
	    long result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=result * x;
	        x=x*x;
	        n=n/2;
	    }
	    return result;
	}
	
	public static int modularExponentiation(int x,int n,int M)
	{
	    int result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=(result * x)%M;
	        x=(x*x)%M;
	        n=n/2;
	    }
	    return result;
	}
	
	public static long modularExponentiation(long x,long n,long M)
	{
	    long result=1;
	    while(n>0)
	    {
	        if(n % 2 ==1)
	            result=(result * x)%M;
	        x=(x*x)%M;
	        n=n/2;
	    }
	    return result;
	}
	
	public static int modInverse(int A,int M)
	{
	    return modularExponentiation(A,M-2,M);
	}
	
	public static long modInverse(long A,long M)
	{
	    return modularExponentiation(A,M-2,M);
	}
	
	public static boolean isPrime(int n)
	{
	    
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	    
	    if (n%2 == 0 || n%3 == 0) 
	    	return false;
	 
	    for (int i=5; i*i<=n; i=i+6)
	    {
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	    }
	    
	    return true;
	}
	
	static class pair 
	{
		Double x, y;
		pair(double x,double y)
		{
			this.x=x;
			this.y=y;
		}
	}
	public static double[] v;
	public static double[] x;
	public static int n;
	public static boolean check(double time)
	{
		pair interval = new pair(Double.MIN_VALUE,Double.MAX_VALUE);
		for(int i=0;i<n;i++)
		{
			double left = x[i] - v[i]*time;
			double right = x[i] + v[i]*time;
			
			if(right<interval.x || left>interval.y)
				return false;
			else 
			{
				interval.x = Math.max(left, interval.x);
				interval.y = Math.min(right, interval.y);
			}
		}
		return true;
	}
	public static double binarySearch()
	{
		double start = 0;
		double end = Math.pow(10, 18);
		double ans = 0;
		while(start<=end)
		{
			double mid = (start+end)/(double)2;
			if(check(mid))
			{
				ans = mid;
				end = mid - 0.0000001;
			}
			else
				start = mid + 0.0000001;
		}
		return ans;
	}
	public static void main(String[] args)
	{
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		n = in.nextInt();
		x = new double[n];
		v = new double[n];
		
		for(int i=0;i<n;i++)
			x[i] = (double)in.nextInt();
		
		for(int i=0;i<n;i++)
			v[i] = (double)in.nextInt();
		
		pw.println(binarySearch());
		pw.flush();
		pw.close();
	}
}