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.io.*;
import java.math.BigInteger;
import java.util.*;

public class MainA {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long mod = 1000000000 + 7;
	static long count=0;
	
	public static int dfs( int v, int vis[], ArrayList<Integer> arr[])
	{
		vis[v]=1;int sum=0;
		for(int i=0;i<arr[v].size();i++)
		{
			int x=arr[v].get(i);
			if(vis[x]==0)
			{
				sum+=dfs(x,vis,arr);
			}
		}
		if((sum+1)%2==0)count++;
		return sum+1;
	}
	private static void soln() 
	{
		int n=nextInt();
		
		int x[]=new int[n];int v[]=new int[n];
		
		for(int i=0;i<n;i++) {x[i]=nextInt();}
		for(int i=0;i<n;i++) {v[i]=nextInt();}
		
		double ans=bSearch(x,v,n);

		pw.printf("%.8f",ans);
	}
	
	public static double bSearch(int x[],int v[],int n)
	{
		double l=0;double r=(double)1e9;

		double eps=(double)1e-7;
		while(l+eps<r)
		{
			double mid=(l+r)/2.0;
			double min = Long.MIN_VALUE, max = Long.MAX_VALUE;
            for (int i = 0; i < n && min <= max; i++) {
                double toleft = x[i] - v[i] * mid;
                double toright = x[i] + v[i] * mid;
                min = Math.max(min, toleft);
                max = Math.min(max, toright);
            }
			if(min<=max)
			{
				r=mid;
			}
			else l=mid;
			
		}
		return r;
	}
	
	public static boolean f(double t,int a[],int b[],long p,int n)
	{
		double totalCons=0;
		for(int i=0;i<n;i++)
		{
			double total=a[i]*t-b[i];
			//pw.printf("%f\n", total);
			if(total>0)
			{
				totalCons+=total;
			}
		}
		//pw.printf("%f %f\n",totalCons,p*t);
		if(totalCons<=p*t)return true;
		else return false;
	}
	public static int check(String s[],int x, int y,int n,int m)
	{
		int dx[]= {-1,0,1,1,1,0,-1,-1};
		int dy[]= {-1,-1,-1,0,1,1,1,0};
		int count=0;
		for(int i=0;i<8;i++)
		{
			int vx=x+dx[i];
			int vy=y+dy[i];
			if(vx<0 || vx>=n ||vy<0 || vy>=m)
			{
				
			}
			else
			{
				if(s[vx].charAt(vy)=='*')count++;
			}
		}
		return count;
	}

	public static class Segment {
		private int[] tree;
		private boolean[] lazy;
		private int size;
		private int n;

		private class node {
			private int a;
			private int b;
			private int c;

			public node(int x, int y, int z) {
				a = x;
				b = y;
				c = z;
			}
		}

		public Segment(int n) {
			//this.base=arr;
			int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
			size = 2 * (int) Math.pow(2, x) - 1;
			tree = new int[size];
			lazy = new boolean[size];
			this.n = n;
			build(0, 0, n - 1);
		}

		public void build(int id, int l, int r) {
			if (l == r) {
				return;
			}
			int mid = (l + r) / 2;
			build(2 * id + 1, l, mid);
			build(2 * id + 2, mid + 1, r);
			tree[id] = tree[2 * id + 1] + tree[2 * id + 2];
		}

		public int query(int l, int r) {
			return queryUtil(l, r, 0, 0, n - 1);
		}

		private int queryUtil(int x, int y, int id, int l, int r) {
			if (l > y || x > r)
				return 0;
			if (x <= l && r <= y) {
				//if(!lazy[id])
				return tree[id];
				//else
				//	return tree[id][0];
			}
			int mid = l + (r - l) / 2;
			shift(id);
			return queryUtil(x, y, 2 * id + 1, l, mid) + queryUtil(x, y, 2 * id + 2, mid + 1, r);
		}

		public void update(int x, int y, int colour, int id, int l, int r) {
			//System.out.println(l+" "+r+" "+x);
			if (x > r || y < l)
				return;
			if (x <= l && r <= y) {

				return;
			}
			int mid = l + (r - l) / 2;
			shift(id);
			update(x, y, colour, 2 * id + 1, l, mid);
			update(x, y, colour, 2 * id + 2, mid + 1, r);
			tree[id] = tree[2 * id + 1] + tree[2 * id + 2];
		}

		public void shift(int id) {

		}
	}

	public static void fft(double[] a, double[] b, boolean invert) {
		int count = a.length;
		for (int i = 1, j = 0; i < count; i++) {
			int bit = count >> 1;
			for (; j >= bit; bit >>= 1)
				j -= bit;
			j += bit;
			if (i < j) {
				double temp = a[i];
				a[i] = a[j];
				a[j] = temp;
				temp = b[i];
				b[i] = b[j];
				b[j] = temp;
			}
		}
		for (int len = 2; len <= count; len <<= 1) {
			int halfLen = len >> 1;
			double angle = 2 * Math.PI / len;
			if (invert)
				angle = -angle;
			double wLenA = Math.cos(angle), wLenB = Math.sin(angle);
			for (int i = 0; i < count; i += len) {
				double wA = 1, wB = 0;
				for (int j = 0; j < halfLen; j++) {
					double uA = a[i + j], uB = b[i + j];
					double vA = a[i + j + halfLen] * wA - b[i + j + halfLen] * wB;
					double vB = a[i + j + halfLen] * wB + b[i + j + halfLen] * wA;
					a[i + j] = uA + vA;
					b[i + j] = uB + vB;
					a[i + j + halfLen] = uA - vA;
					b[i + j + halfLen] = uB - vB;
					double nextWA = wA * wLenA - wB * wLenB;
					wB = wA * wLenB + wB * wLenA;
					wA = nextWA;
				}
			}
		}
		if (invert) {
			for (int i = 0; i < count; i++) {
				a[i] /= count;
				b[i] /= count;
			}
		}
	}

	static void multiply(long[][] a, long[][] b, long m) {
		int n = a.length;
		long[][] mul = new long[n][n];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < n; j++) {
				mul[i][j] = 0;
				for (int k = 0; k < n; k++)
					mul[i][j] = (mul[i][j] + (a[i][k] * b[k][j]) % m) % m;
			}
		}
		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++)
				a[i][j] = mul[i][j];
	}

	private static 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 static 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()
		//			{
		//				/*try { 
		//					InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\B-large-practice.in")); 
		//				} catch (FileNotFoundException e) { // TODO Auto-generated catch block
		//					e.printStackTrace(); 
		//				} */
		//				InputReader(System.in);
		//				pw = new PrintWriter(System.out);
		//				/*try { 
		//					pw=new PrintWriter(new FileOutputStream("C:\\Users\\hardik\\Desktop\\out.txt")); 
		//				} catch (FileNotFoundException e) { // TODO Auto-generated catch block
		//					e.printStackTrace();
		//				}*/
		//				soln();
		//				pw.close();
		//			}
		//		}, "1", 1 << 26).start();

		/*try { 
			InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\B-large-practice.in")); 
		} catch (FileNotFoundException e) { // TODO Auto-generated catch block
			e.printStackTrace(); 
		} */
		InputReader(System.in);
		pw = new PrintWriter(System.out);
		/*try { 
			pw=new PrintWriter(new FileOutputStream("C:\\Users\\hardik\\Desktop\\out.txt")); 
		} catch (FileNotFoundException e) { // TODO Auto-generated catch block
			e.printStackTrace();
		}*/
		soln();
		pw.close();
	}

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

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

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

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

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

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

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

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

	private static 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);
	}
}