Problem: Barney lives in country USC (United States of Charzeh). USC has n cities numbered from 1 through n and n - 1 roads between them. Cities and roads of USC form a rooted tree (Barney's not sure why it is rooted). Root of the tree is the city number 1. Thus if one will start his journey from city 1, he can visit any city he wants by following roads.

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Some girl has stolen Barney's heart, and Barney wants to find her. He starts looking for in the root of the tree and (since he is Barney Stinson not a random guy), he uses a random DFS to search in the cities. A pseudo code of this algorithm is as follows:
    
    
      
    let starting_time be an array of length n  
    current_time = 0  
    dfs(v):  
    	current_time = current_time + 1  
    	starting_time[v] = current_time  
    	shuffle children[v] randomly (each permutation with equal possibility)  
    	// children[v] is vector of children cities of city v  
    	for u in children[v]:  
    		dfs(u)  
    

As told before, Barney will start his journey in the root of the tree (equivalent to call dfs(1)).

Now Barney needs to pack a backpack and so he wants to know more about his upcoming journey: for every city i, Barney wants to know the expected value of starting_time[i]. He's a friend of Jon Snow and knows nothing, that's why he asked for your help.

Input

The first line of input contains a single integer n (1 ≤ n ≤ 105) — the number of cities in USC.

The second line contains n - 1 integers p2, p3, ..., pn (1 ≤ pi < i), where pi is the number of the parent city of city number i in the tree, meaning there is a road between cities numbered pi and i in USC.

Output

In the first and only line of output print n numbers, where i-th number is the expected value of starting_time[i].

Your answer for each city will be considered correct if its absolute or relative error does not exceed 10 - 6.

Examples

Input

7
1 2 1 1 4 4


Output

1.0 4.0 5.0 3.5 4.5 5.0 5.0 


Input

12
1 1 2 2 4 4 3 3 1 10 8


Output

1.0 5.0 5.5 6.5 7.5 8.0 8.0 7.0 7.5 6.5 7.5 8.0 

Solution (in JAVA):

Solution:
/**
 p * @author prakhar28
 *
 */
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.text.*;
import java.math.*;
import java.util.regex.*;


import java.io.IOException;
import java.nio.file.Files;
import java.nio.file.Paths;

public class Main{
	
	static class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
 
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[200005]; // line length+1
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n' || c==' ') {
                	//buf[cnt++]=(byte)c;
                    break;
                }
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
 
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
	
	static class FastScanner {

	    private final BufferedReader bufferedReader;
	    private StringTokenizer stringTokenizer;

	    public FastScanner() {
	        bufferedReader = new BufferedReader(new InputStreamReader(System.in));
	    }

	    public String next() {
	        while (stringTokenizer == null || !stringTokenizer.hasMoreElements()) {
	            try {
	                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
	            } catch (IOException e) {
	                throw new RuntimeException("Can't read next value", e);
	            }
	        }
	        return stringTokenizer.nextToken();
	    }

	    public int nextInt() {
	        return Integer.parseInt(next());
	    }

	    public long nextLong() {
	        return Long.parseLong(next());
	    }

	    public double nextDouble() {
	        return Double.parseDouble(next());
	    }

	    public String nextLine(){
	        String str = "";
	        try {
	            str = bufferedReader.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
	    }
	}
	
	static void closeall() throws IOException{
		printWriter.close();
		sc.close();
		in.close();
	}
	static Scanner sc = new Scanner(System.in);
	static Reader in = new Reader();
	static FastScanner fastScanner = new FastScanner();
	static PrintWriter printWriter = new PrintWriter(new BufferedOutputStream(System.out));
	static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
	static long INF = (long)(1e18);

	
	int V,E;
	ArrayList<Integer> adj[];
	Main(int v){
		V=v;
		adj=new ArrayList[v];
		for(int i=0;i<v;i++)
			adj[i] = new ArrayList<>();
	}
	void addEdge(int u,int v){
		adj[u].add(v);
		//adj[v].add(u);
	}
	
	
	static long power(long a,long k)
	{
		long m = 1000000007;
	    long ans=1;
	    long tmp=a%m;
	    while(k>0)
	    {
	        if(k%2==1)
	        	ans=ans*tmp%m;
	        tmp=tmp*tmp%m;
	        k>>=1;
	    }
	    return ans;
	}
	
	static class Pair implements Comparable<Pair>{
		int a,b;
		Pair(int a,int b){
			this.a=a;
			this.b=b;
		}
		public int compareTo(Pair ob){
			return this.b-ob.b;
		}
		
	}
	static int gcd(int a,int b) {
		if(a<b) {
			int t = a;
			a = b;
			b = t;
		}
		int r = a%b;
		if(r==0)
			return b;
		return gcd(b,r);
	}
	
	static int lower_bound(int[] a,int low,int high,int val) {
		while(low!=high) {
			int mid = (low+high)/2;
			if(a[mid]<val)
				low=mid+1;
			else
				high=mid;
		}
		return low;
	}
	
	static int max(int a,int b) {
		return (int)Math.max(a, b);
	}
	static long max(long a,long b) {
		return (long)Math.max(a, b);
	}
	static long min(long a,long b) {
		return (long)Math.min(a, b);
	}
	static int min(int a,int b) {
		if(a<b)
			return a;
		return b;
	}
	static long m = 1000000007;
	
	
	public static void main(String args[])throws IOException{
		int n = in.nextInt();
		Main ob = new Main(n);
		for(int i=1;i<=n-1;i++) {
			int x = in.nextInt() - 1;
			ob.addEdge(x, i);
		}
		int[] c = new int[n];
		Arrays.fill(c, 1);
		ob.dfs(0,c);
		double ans[] = new double[n];
		ans[0]=1;
		ob.getans(ans,c,0);
		for(int i=0;i<n;i++)
			printWriter.print(ans[i]+" ");
		closeall();
	}
	int dfs(int s,int[] c) {
		for(int i=0;i<adj[s].size();i++)
			c[s]+=dfs(adj[s].get(i),c);
		return c[s];
	}
	void getans(double[] ans,int[] c,int cur) {
		double sum = 0;
		for(int i=0;i<adj[cur].size();i++)
			sum+=c[adj[cur].get(i)];
		double z = ans[cur]+1;
		double d = 0;
		double n = adj[cur].size();
		if(n>1) 
			d = 0.5;
		for(int i=0;i<adj[cur].size();i++) 
			ans[adj[cur].get(i)]=z+(sum-c[adj[cur].get(i)])*d;
		
		for(int i=0;i<adj[cur].size();i++)
			getans(ans,c,adj[cur].get(i));
	}
}