Problem: When Sasha was studying in the seventh grade, he started listening to music a lot. In order to evaluate which songs he likes more, he introduced the notion of the song's prettiness. The title of the song is a word consisting of uppercase Latin letters. The prettiness of the song is the prettiness of its title.

Let's define the simple prettiness of a word as the ratio of the number of vowels in the word to the number of all letters in the word.

Let's define the prettiness of a word as the sum of simple prettiness of all the substrings of the word.

More formally, let's define the function vowel(c) which is equal to 1, if c is a vowel, and to 0 otherwise. Let si be the i-th character of string s, and si..j be the substring of word s, staring at the i-th character and ending at the j-th character (sisi + 1... sj, i ≤ j).

Then the simple prettiness of s is defined by the formula:

<image>

The prettiness of s equals 

<image>

Find the prettiness of the given song title.

We assume that the vowels are I, E, A, O, U, Y.

Input

The input contains a single string s (1 ≤ |s| ≤ 5·105) — the title of the song.

Output

Print the prettiness of the song with the absolute or relative error of at most 10 - 6.

Examples

Input

IEAIAIO


Output

28.0000000


Input

BYOB


Output

5.8333333


Input

YISVOWEL


Output

17.0500000

Note

In the first sample all letters are vowels. The simple prettiness of each substring is 1. The word of length 7 has 28 substrings. So, the prettiness of the song equals to 28.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

import static java.lang.Math.*;

public class Main {
    FastScanner in;
    PrintWriter out;

    static final String FILE = "";

    boolean isMelodic(char c) {
        return (c == 'I' || c == 'E' || c == 'A' || c == 'O' ||
                c == 'U' || c == 'Y');
    }

    public void solve() {
        while (true) {
            String s = in.next();
            int n = s.length();
            int ms[] = new int[n];
            long ans[] = new long[n];
            long down[] = new long[n];
            long up[] = new long[n];
            long all[] = new long[n];
            long sumAll = 0;

            // precalc
            for (int i = 0; i < s.length(); i++) {
                if (isMelodic(s.charAt(i))) {
                    ms[i] = 1;
                    int gran = min(i + 1, n - i);
                    int downGran = max(i + 1, n - i);
                    down[gran - 1]++;
                    sumAll += gran;
                    if (gran - 1 >= 0)
                        all[gran - 1] -= gran;
                    up[n - 1] += n - downGran;
                }
            }

            for (int i = n - 2; i >= 0; i--) {
                up[i] += max(0, up[i + 1] - 1);
            }

            // calc
            long currDown = 0;
            long currUp = 0;
            long currAll = sumAll;
            for (int i = n - 1; i >= 0; i--) {
                currDown += down[i];
                currAll += all[i];
                ans[i] += currDown * (i + 1);
                ans[i] += currAll;
            }

            for (int i = n - 1; i >= 0; i--) {
                ans[i] = ans[n - 1 - i];
            }

            double sum = 0;
            for (int i = 0; i < n; i++) {
                //out.print(ans[i] + " ");
                sum += (double) (ans[i]) / (double) (i + 1);
            }
            //out.println();
            out.println(sum);
            //out.flush();
            break;
        }
    }

    public void run() {
        if (FILE.equals("")) {
            in = new FastScanner(System.in);
            out = new PrintWriter(System.out);
        } else {
            try {
                in = new FastScanner(new FileInputStream(FILE +
                        ".in"));
                out = new PrintWriter(new FileOutputStream(FILE +
                        ".out"));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }
        solve();
        out.close();
    }

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

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return "";
            }
        }

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

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

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

        public float nextFloat() {
            return Float.parseFloat(next());
        }
    }

    class Pair<A extends Comparable<A>, B extends Comparable<B>>
            implements Comparable<Pair<A, B>> {
        public A a;
        public B b;

        public Pair(A a, B b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Pair<A, B> o) {
            if (o == null || o.getClass() != getClass())
                return 1;
            int cmp = a.compareTo(o.a);
            if (cmp == 0)
                return b.compareTo(o.b);
            return cmp;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Pair<?, ?> pair = (Pair<?, ?>) o;

            if (a != null ? !a.equals(pair.a) : pair.a != null) return
                    false;
            return !(b != null ? !b.equals(pair.b) : pair.b != null);
        }
    }

    class PairInt extends Pair<Integer, Integer> {
        public PairInt(Integer u, Integer v) {
            super(u, v);
        }
    }

}