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:
import java.util.*;
import java.math.*;
import java.io.*;
public class Luck{
	public static InputReader sc;
    public static PrintWriter out;
    public static final long MOD = (long) (1e9 + 7);
    public static void main(String[] args){
    	sc=new InputReader(System.in);	
    	out=new PrintWriter(System.out);    	
    	int n=sc.nextInt();
    	long[] X=new long[n];
    	long[] V=new long[n];
    	long min=Long.MAX_VALUE;
    	long max=Long.MIN_VALUE;
    	for(int i=0;i<n;i++){
    		X[i]=sc.nextLong();
    		if(X[i]<min){
    			min=X[i];
    		}
    		if(X[i]>max){
    			max=X[i];
    		}
    	}
    	for(int i=0;i<n;i++){
    		V[i]=sc.nextLong();
    	}
    	double l=(double)0;
    	double r=(double)1e18;
    	int count=0;
    	while(count<1010){
    		count+=1;
    		double mid1=l+(r-l)/3D;
    		double mid2=l+(r-l)/3D*2D;
    		double val1=check(X,V,mid1);
    		double val2=check(X,V,mid2);
    		//out.println("val: "+val1+" "+val2);
    		if(val1<val2){
    			r=mid2;
    		}
    		else{
    			l=mid1;
    		}
    	}
    	out.println(check(X,V,r));
    	out.close();
    }
    static double check(long[] X,long[] V,double des){
    	double max=Double.MIN_VALUE;
    	for(int i=0;i<X.length;i++){
    		double time=(double)Math.abs(X[i]-des)/(double)V[i];
//    		out.print((float)Math.abs(X[i]-des)+" "+(float)V[i]+" ");
//    		out.println(time+" ");
    		if(time>max){
    			max=time;
    		}
    	}
    	return max;
    }
    static class Pair{
    	int row;
    	int col;
    	int hour;
    	Pair(){
    		this.row=-1;
    		this.col=-1;
    	}
    	Pair(int s,int e,int h){
    		this.row=s;
    		this.col=e;
    		this.hour=h;
    	}
//    	public static Comparator<Pair> Val=new Comparator<Pair>(){
//    		public int compare(Pair p1,Pair p2){
//    			return (int)p1.cost-(int)p2.cost;
//    		}
//    	};
    }
//    static int val;
//    static class DisjointSet{
//    	int n;
//    	int[] par;
//    	int[] rank;
//    	DisjointSet(int n){
//    		this.n=n;
//    		this.par=new int[n];
//    		this.rank=new int[n];
//    		makeSet();
//    	}
//    	void makeSet(){
//    		for(int i=1;i<n;i++){
//    			par[i]=i;
//    			rank[i]=1;
//    		}
//    	}
//    	void union(int x,int y){
//    		int parX=parent(x);
//    		int parY=parent(y);
//    		if(parX!=parY){
//    			if(rank[parX]>=rank[parY]){
//    				rank[parX]+=rank[parY];
//    				rank[parY]=0;
//    				par[parY]=parX;
//    			}
//    			else{
//    				rank[parY]+=rank[parX];
//    				rank[parX]=0;
//    				par[parX]=parY;
//    			}
//    			val-=1;
//    		}
//    	}
//    	int parent(int c){
//    		int i=c;
//    		while(i!=par[i]){
//    			i=par[i];
//    		}
//    		return i;
//    	}
//    }
    static int gcd(int a,int b){
    	if(b==0){
    		return a;
    	}
    	return gcd(b,a%b);
    	
    }
    static int lcm(int a,int b){
    	int g;
    	if(a<b){
    		g=gcd(b,a);
    	}
    	else{
    		g=gcd(a,b);
    	}
    	return (a*b)/g;
    }
    static long bigmod ( long a, long p, long m ) {
        long res = 1 % m, x = a % m;
        while ( p>0 ) {
            if ( (p & 1)==1 ) res = ( res * x ) % m;
            x = ( x * x ) % m; p >>= 1;
        }
        return res;
    }
    static boolean isPrime(int n){
    	 if (n == 2)
    	        return true;
    	    for (long i = 2; i * i <= n; i++) {
    	        if (n % i == 0)
    	            return false;
    	    }
    	    return true;
    }
    
    static void shuffle(int[] A){
    	for(int i=A.length-1;i>0;i--){
    		int j=(int)(Math.random()*(i+1));
    		int temp=A[j];
    		A[j]=A[i];
    		A[i]=temp;
    	}
    }
    
	public static class Node implements Comparable<Node>{
	    int u;
	    int v;
	    public Node(){
	    	;
	    }
	    public Node (int u, int v) {
	    	this.u = u;
	        this.v = v;
	    }
	    
	    public void print() {
	        out.println(v + " " + u + " ");
	    }
	   
	    public int compareTo(Node n1){
	    	return this.u-n1.u;
	    }
	}
	public static long pow(long base,long exp,long mod){
		if(exp==0){
			return 1;
		}
		if(exp==1){
			return base;
		}
		long temp=exp/2;
		long val=pow(base,temp,mod);
		long result=val*val;
		result=(result%mod);
		long AND=exp&1;
		if(AND==1){
			result*=base;
			result=(result%mod);
		}
		return result;
	}
	public static BigInteger pow(BigInteger base, BigInteger exp) {
	    if(exp.equals(new BigInteger(String.valueOf(0)))){
	        return new BigInteger(String.valueOf(1));
	    }    
	    if(exp.equals(new BigInteger(String.valueOf(1))))
	        return base;
	    BigInteger temp=exp.divide(new BigInteger(String.valueOf(2)));
	    BigInteger val = pow(base, temp);
	    BigInteger result = val.multiply(val);
	    result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    BigInteger AND=exp.and(new BigInteger(String.valueOf(1)));
	    if(AND.equals(new BigInteger(String.valueOf(1)))){
	        result = result.multiply(base);
	        result=result.remainder(new BigInteger(String.valueOf(MOD)));
	    }    
	    return result;
	}
	    
	static class InputReader {

	    private InputStream stream;
	    private 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 boolean isSpaceChar(int c) {
	        if (filter != null)
	            return filter.isSpaceChar(c);
	        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	    }

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

}