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:
import java.io.*;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class Main {
    private FastScanner in;
    private PrintWriter out;

    private void solve() throws IOException {
        int n = in.nextInt();
        ArrayList<Integer> ch[] = new ArrayList[n];
        for (int i = 0; i < ch.length; i++) {
            ch[i] = new ArrayList<>();
        }
        int[] p = new int[n];
        double[] ans = new double[n];
        for (int i = 1; i < n; i++) {
            p[i] = in.nextInt() - 1;
            ch[p[i]].add(i);
        }
//        double[] fact = new double[111111];
//        fact[0] = 1;
//        for (int i = 1; i < fact.length; i++) {
//            fact[i] = fact[i - 1] * i;
//        }
//        double[] mul = new double[111111];
//        for (int i = 2; i < 100; i++) {
//            double kek = 1. / i;
//            mul[i] = kek;
//            for (int j = i - 1; j > 1; j--) {
//                kek /= j;
//                mul[i] += kek * fact[i - 2] / fact[i - 2 - (i - j)];
//            }
//        }
        int[] size = new int[n];
        solve(0, p, ans, ch, size);
        for (int i = 0; i < ans.length; i++) {
            out.printf("%.15f ", ans[i]);
        }
        out.println();
    }

    private void solve(int v, int[] p, double[] ans, ArrayList<Integer>[] ch, int[] size) {
        if (v == 0) {
            ans[v] = 1;
        } else {
            ans[v] = 1 + ans[p[v]] + (countSize(p[v], ch, size) - countSize(v, ch, size) - 1) / 2.;
        }
        for (int to : ch[v]) {
            solve(to, p, ans, ch, size);
        }
    }

    private int countSize(int v, ArrayList<Integer>[] ch, int[] size) {
        if (size[v] == 0) {
            size[v] = 1;
            for (int to : ch[v]) {
                size[v] += countSize(to, ch, size);
            }
        }
        return size[v];
    }

    private void run() throws IOException {
        in = new FastScanner();
        out = new PrintWriter(System.out, false);
        solve();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Main().run();
    }
}

class FastScanner {
    private final BufferedReader br;
    private StringTokenizer st;
    private String last;

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

    public FastScanner(String path) throws IOException {
        br = new BufferedReader(new FileReader(path));
    }

    public FastScanner(String path, String decoder) throws IOException {
        br = new BufferedReader(new InputStreamReader(new FileInputStream(path), decoder));
    }

    String next() throws IOException {
        while (st == null || !st.hasMoreElements())
            st = new StringTokenizer(br.readLine());
        last = null;
        return st.nextToken();
    }

    String nextLine() throws IOException {
        st = null;
        return (last == null) ? br.readLine() : last;
    }

    boolean hasNext() {
        if (st != null && st.hasMoreElements())
            return true;

        try {
            while (st == null || !st.hasMoreElements()) {
                last = br.readLine();
                st = new StringTokenizer(last);
            }
        } catch (Exception e) {
            return false;
        }

        return true;
    }

    String[] nextStrings(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = next();
        return arr;
    }

    String[] nextLines(int n) throws IOException {
        String[] arr = new String[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLine();
        return arr;
    }

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

    int[] nextInts(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    Integer[] nextIntegers(int n) throws IOException {
        Integer[] arr = new Integer[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextInt();
        return arr;
    }

    int[][] next2Ints(int n, int m) throws IOException {
        int[][] arr = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextInt();
        return arr;
    }

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

    long[] nextLongs(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++)
            arr[i] = nextLong();
        return arr;
    }

    long[][] next2Longs(int n, int m) throws IOException {
        long[][] arr = new long[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                arr[i][j] = nextLong();
        return arr;
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(next().replace(',', '.'));
    }

    double[] nextDoubles(int size) throws IOException {
        double[] arr = new double[size];
        for (int i = 0; i < size; i++)
            arr[i] = nextDouble();
        return arr;
    }

    boolean nextBool() throws IOException {
        String s = next();
        if (s.equalsIgnoreCase("true") || s.equals("1"))
            return true;

        if (s.equalsIgnoreCase("false") || s.equals("0"))
            return false;

        throw new IOException("Boolean expected, String found!");
    }
}