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.awt.List;
import java.io.*;
import java.util.*;




/*
 * kishan Thesiya
 * daiict
 * kishanthesiya25@gmail.com
 * 
 * 
 */


public class Main {
	FastScanner in;
	PrintWriter out;

	static ArrayList[] adj;
	static int n;
	static int x;
	static int visited[][];
	static int Ad[];
	static int Bd[];
 
	static int brr[][];
	static int a;
	static int b;
	static int parent[];
	static int size[];
	long mod = (long)1e9+7;
//Segment tree do not delete
	static int arr[];	
	static int d[];
	static int h;
// till now	

	class Segment{
	  private  int Lazy[];
	 
	    void ans(){
	   
	    	
	     int x = (int) (Math.ceil(Math.log(100000) / Math.log(2)));
	        int max_size = 2 * (int) Math.pow(2, x) - 1;
	        int SegTree[][] = new int[max_size][3]; // allocate memory
	        Lazy = new int[max_size];
	        
	       String s = in.next();
	       n = s.length();
	        
	        int q=in.nextInt();
	        

	        build_ST(0, 0, n - 1,SegTree,s);
	  
	        for(int i = 0;i<2*n;i++){
	        	System.out.println(SegTree[i][0] + " " + SegTree[i][1] + " " + SegTree[i][2] + " " + (i+n));
	        }
	        
	        while(q-->0)
	        {
	          int a = in.nextInt();
	          int b = in.nextInt();
	          
	          int d = getMaxST(0, n-1, a-1, b-1, 0,SegTree);
	          System.out.println(d);
	        }
	    }
	    
	    
	 void build_ST(int node, int start, int end,int SegTree[][],String s) 
	   {
	    if(start > end) return; 
	  	if(start == end) { 
	  		System.out.println(start + " " + node);
	  		if(s.charAt(start) == '('){
	  			SegTree[node][1] = 1;
	  		}else{
	  			SegTree[node][2] = 1;
	  		}
	  		
			return;
		}
		int mid=(start + end) >> 1;
		build_ST(node*2+1, start, mid, SegTree,s); // Init left child
		build_ST(node*2+2, 1+mid, end,SegTree,s); // Init right child
		
		// Init root value
		
		int t = Math.min(SegTree[2*node + 1][1], SegTree[2*node+2][2]);
		
		SegTree[node][0] = SegTree[2*node+1][0] + SegTree[2*node+2][0] + 2*t;
		SegTree[node][1] = SegTree[2*node+1][1] + SegTree[2*node+2][1] - t;
		SegTree[node][2] = SegTree[2*node+1][2] + SegTree[2*node+2][2] - t;
		
		
	}
//	    void update_ST(int node, int start, int end, int l, int r, int diff) {
//	        if(Lazy[node] != 0)
//	        {
//	            int pending = Lazy[node];
//	            
//	            SegTree[node] -= pending;
//	            
//	           if(start != end)
//	            {
//	                Lazy[2 * node + 1] += Lazy[node];
//	                Lazy[2 * node + 2] += Lazy[node];
//	            }
//	           Lazy[node] = 0;
//	        }
//	        if (end < l || start > r)
//	            return ;
//	          if(l<=start && end<=r)
//	        {
//	        	  SegTree[node] -= diff;
//	               
//	            if(start != end) // not a leaf
//	            {
//	                Lazy[2*node+1] += diff;
//	                Lazy[2*node+2] += diff;
//	            }
//	            return;
//	        }
//	        int mid=(start + end) >> 1;
//		update_ST(node*2+1, start, mid, l, r, diff); // Updating left child
//		update_ST(2+node*2, 1+mid, end, l, r, diff); // Updating right child
//	
//		SegTree[node] = Math.max(SegTree[node*2+1],SegTree[node*2+2]); 
//		
//	    }
	      int getMaxST(int start, int end, int l, int r, int node,int SegTree[][])
	    {
//	    	  if(Lazy[node] != 0)
//		        {
//		            int pending = Lazy[node];
//		            
//		            SegTree[node] -= pending;
//		            
//		           if(start != end)
//		            {
//		                Lazy[2 * node + 1] += Lazy[node];
//		                Lazy[2 * node + 2] += Lazy[node];
//		            }
//		           Lazy[node] = 0;
//		        }
	        if (l <= start && r >= end)
	            return SegTree[node][0];
	         if (end < l || start > r)
	            return 0;
	        int mid = (start + end) >> 1;
	        return getMaxST(start, mid, l, r, 2 * node + 1,SegTree)+getMaxST(mid + 1, end, l, r, 2 * node + 2,SegTree);
	    }
	      
	}
	
	static class Pair implements Comparable<Pair>
    {
        int x;
        int y;
        
        Pair(int l, int m) {
            this.x = l;
            this.y = m;
        }
        
        public int compareTo(Pair p) {
            if (this.x == p.x) {
                return (int)(this.y-p.y);
            }
            return (int)(this.x - p.x);
        }
        
        public String toString(){
        	return x + " " + y;
        }
        
        public boolean equals(Object o){
        	if(o instanceof Pair){
        		Pair a = (Pair)o;
        		
        		return this.x == a.x && this.y == a.y;
        	}
        	
        	return false;
        }
        
        public int hashCode(){
        	return new Long(x).hashCode()*31 + new Long(y).hashCode();
        }
    
    }
    
	
	public static int gcd(int a, int b) {
		if (b == 0) return a;
		return gcd(b, a%b);
	}
	
	public static int find(int i){
		if(parent[i] != i){
			return find(parent[i]);
		}
		
		return i;
	}
	
	
	public static void union(int a,int b){
		int ra = find(a);
		int rb = find(b);

		if(ra!= rb){
			if(size[ra] > size[rb]){
				parent[rb] =ra;
				size[ra] += size[rb];
			}else{
				parent[ra] = rb;
				size[rb] += size[ra];
			}
		}
		
	}

	public static void apply(int p,int value){
		arr[p] += value;
		
		if(p < n){
			d[p] += value;
		}
	}
	
	public static void push(int p){
		
		for(int s = h;s>0;s--){
			int i = p >> s;
			
			if(d[i] != 0){
				apply(i<<1,d[i]);
				apply(i<<1|1,d[i]);
				d[i] = 0;
			}		
		}		
	}
	
	public static void lazybuild(int p){
		while(p > 1){
			p>>=1;
			arr[p] = Math.max(arr[p<<1], arr[p<<1|1]) + d[p];
		}
	}
	
	public static void lazyupdate(int l,int r,int value){
		l += n; r += n+1;		
		int l0 = l;int r0 = r;
		for(;l<r; l>>=1,r>>=1){
			if((l&1) == 1){
				apply(l++,value);
			}
			
			if((r&1) == 1){
				apply(--r,value);
			}
		}
		lazybuild(l0);
		lazybuild(r0-1);
			
	}
	
	public static int lazyquery(int l,int r){
		l += n;r += n+1;
		push(l);push(r-1);
		int res = (int)-2e9;
		
		for(;l<r;l>>=1,r>>=1){
			if((l&1) == 1){
				res = Math.max(arr[l++], res);
			}
			
			if((r&1) == 1){
				res = Math.max(arr[--r], res);
			}
		}
		
		return res;
	}
	
	public static void build(){
		
		for(int i = n-1;i>0;i--){
			arr[i] = Math.max(arr[i<<1], arr[i<<1|1]);
		}
		
	}
	
	public static void update(int p,int v){
		
		for(arr[p += n] = v; p>0; p>>=1 ){
			arr[p>>1] = Math.max(arr[p], arr[p^1]);
		}
		
	}
	
	public static int query(int l,int r){
		
		r++;
		int max = 0;
		for(l +=n,r +=n;l<r; l>>=1,r>>=1 ){
			
		
			
			if((l&1) == 1){
				max = Math.max(max, arr[l++]);
			}
			
			if((r&1) == 1){
				max = Math.max(max, arr[--r]);
			}
		}
		
		return max;
	}
	
	void multiply(long a[][], long b[][])
	{
	    
	    long mul[][] = new long[3][3];
	    for (int i = 0; i < 3; i++)
	    {
	        for (int j = 0; j < 3; j++)
	        {
	            mul[i][j] = 0;
	            for (int k = 0; k < 3; k++)
	                mul[i][j] = (int) ((mul[i][j] + (a[i][k]*b[k][j])%mod)%mod);
	        }
	    }
	 
	  
	    for (int i=0; i<3; i++)
	        for (int j=0; j<3; j++)
	            a[i][j] = mul[i][j];  
	}
	
	long power(long F[][], long n)
	{
	    long M[][] = {{1,1,0}, {1,0,0}, {0,1,0}};
	 
	    if (n==1)
	        return (long) ((F[0][0] + F[0][1])%mod);
	 
	    power(F, n/2);
	 
	    multiply(F, F);
	 
	    if (n%2 != 0)
	        multiply(F, M);
	 
	    return (long) ((F[0][0] + F[0][1])%mod) ;
	}
	 
	
	long findNthTerm(long n)
	{
	    long[][] F = {{1,1,0}, {1,0,0}, {0,1,0}} ;
	 
	    return power(F, n);
	}
	 
	
    void solve() throws NumberFormatException, IOException {
 
    	Scanner in = new Scanner(System.in);
   
//    	Segment s = new Segment();
//    	
//    	s.ans();
    	
//    	n = in.nextInt();
//    	arr = new int[2*n];
//    	d = new int[n];
//    	h = (int)Math.ceil((Math.log(n)/Math.log(2)));
//    	for(int i = 0;i<n;i++){
//    		arr[i+n] = in.nextInt();
//    	}
//    	
//    	build();
    	
    	String s = in.nextLine();
    	
    	double res = 0.0;
    	double add = 0.0;
    	double del = 0.0;
    	double cur = 0.0;
    	int n = s.length();
    	
    	for(int i = 1;i<=s.length();i++){
    		add += 1.0/i;
    		cur += 1.0/i;
    	}
    	
    	for(int i = 0;i<s.length();i++){
    		char a = s.charAt(i);
    		
    		if(a == 'A' || a == 'E' || a == 'I' || a=='O' || a=='U' || a=='Y'){
    			res += cur;
    		}
    		
    		add -= 1.0/(n-i);
    		del += 1.0/(i+1);
    		cur += add;
    		cur -= del;
    	}
    	
    	System.out.println(res);
//    	 BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//        
//    	 StringBuilder sb = new StringBuilder();
// 
//    	 int tests = Integer.parseInt(br.readLine().trim());
//    	  
//          while (tests-- > 0) {
//        	 
//        	int n = Integer.parseInt(br.readLine().trim());
//        	String s[] = br.readLine().split(" ");
//        	
//        	long arr[] = new long[n];
//    		
//    		for(int j = 0;j<n;j++){
//    			arr[j] = Long.parseLong(s[j]);
//    		}
//    		
//    		Arrays.sort(arr);
//    		
//    		long min = 0;
//    		long max = 0;
//    		
//    		for(int j = n-2;j>=0;j-=2){
//    			min += Math.abs(arr[j]-arr[j+1]);
//    		}
//    		
//    		for(int j = 0,k=n-1;j<k;j++,k--){
//    			max += Math.abs(arr[j]-arr[k]);
//    		}
//    		
//    		sb.append(min + " " + max + "\n");
//        	  
//          }
//          
//          
//          System.out.println(sb.toString());
//          
//           
//         
}
    
    public static String[] reverse(String arr[]){
    	
    	
    	for(int i = 0;i<arr.length/2;i++){
    		String temp = arr[i];
    		arr[i] = arr[arr.length-i-1];
    		arr[arr.length-1-i] = temp;
    	}
    	
    	return arr;
    	
    }
	
	
    
  
    private static long ans(long n){
        if(n==1) return 2;
        n+=1;
        int cnt=-1;
        while(n%2==0){
            n/=2;
            cnt++;
        }
        if(n==1){
            return (int)Math.pow(2,cnt)-1;
        }
        return -1;
    }
    public static long sum(long x){
    	return x<10?x:x%10 + sum(x/10);
    }
	
	public static long gcd(long x, long y) {
		if (x == 0)
			return y;
		else
			return gcd( y % x,x);
	}
	public static long pow(long n,long p,long m){
        long  result = 1;
         if(p==0)
           return 1;
       if (p==1)
           return n;
       while(p!=0)
       {
           if(p%2==1)
               result *= n;
           if(result>=m)
           result%=m;
           p >>=1;
           n*=n;
           if(n>=m)
           n%=m;
       }
       return result;
       }
	
	
	
	public static boolean isPrime(int n) {
		// Corner cases
		if (n <= 1)
			return false;
		if (n <= 3)
			return true;
 
		// This is checked so that we can skip 
		// middle five numbers in below loop
		if (n % 2 == 0 || n % 3 == 0)
			return false;
 
		for (int i = 5; i * i <= n; i = i + 6)
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
 
		return true;
	}
	

	void run() throws NumberFormatException, IOException {
		in = new FastScanner();
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;

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

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(in.br.readLine());
				} catch (IOException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

		double nextDouble() {
			return Double.parseDouble(next());
		}
	}
	
	class Tri{
		
		Tri[] arr;
		
		public Tri(){
			arr = new Tri[27];
		}
		
	}
	
	
 

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


class SegmentTreeRMQ
{
    long st[]; //array to store segment tree
 
    // A utility function to get minimum of two numbers
    long minVal(long x, long y) {
        return (x < y) ? y : x;
    }
 
    // A utility function to get the middle index from corner
    // indexes.
    int getMid(int s, int e) {
        return s + (e - s) / 2;
    }
 
    /*  A recursive function to get the minimum value in a given
        range of array indexes. The following are parameters for
        this function.
 
        st    --> Pointer to segment tree
        index --> Index of current node in the segment tree. Initially
                   0 is passed as root is always at index 0
        ss & se  --> Starting and ending indexes of the segment
                     represented by current node, i.e., st[index]
        qs & qe  --> Starting and ending indexes of query range */
    long RMQUtil(int ss, int se, int qs, int qe, int index)
    {
        // If segment of this node is a part of given range, then
        // return the min of the segment
        if (qs <= ss && qe >= se)
            return st[index];
 
        // If segment of this node is outside the given range
        if (se < qs || ss > qe)
            return 0;
 
        // If a part of this segment overlaps with the given range
        int mid = getMid(ss, se);
        return minVal(RMQUtil(ss, mid, qs, qe, 2 * index + 1),
                RMQUtil(mid + 1, se, qs, qe, 2 * index + 2));
    }
 
    // Return minimum of elements in range from index qs (quey
    // start) to qe (query end).  It mainly uses RMQUtil()
    long RMQ(int n, int qs, int qe)
    {
        // Check for erroneous input values
        if (qs < 0 || qe > n - 1 || qs > qe) {
         //   System.out.println("Invalid Input");
            return -1;
        }
 
        return RMQUtil(0, n - 1, qs, qe, 0);
    }
 
    // A recursive function that constructs Segment Tree for
    // array[ss..se]. si is index of current node in segment tree st
    long constructSTUtil(long arr[], int ss, int se, int si)
    {
        // If there is one element in array, store it in current
        //  node of segment tree and return
        if (ss == se) {
            st[si] = arr[ss];
            return arr[ss];
        }
 
        // If there are more than one elements, then recur for left and
        // right subtrees and store the minimum of two values in this node
        int mid = getMid(ss, se);
        st[si] = minVal(constructSTUtil(arr, ss, mid, si * 2 + 1),
                constructSTUtil(arr, mid + 1, se, si * 2 + 2));
        return st[si];
    }
 
    /* Function to construct segment tree from given array. This function
       allocates memory for segment tree and calls constructSTUtil() to
       fill the allocated memory */
    void constructST(long arr[], int n)
    {
        // Allocate memory for segment tree
 
        //Height of segment tree
        int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
 
        //Maximum size of segment tree
        int max_size = 2 * (int) Math.pow(2, x) - 1;
        st = new long[max_size]; // allocate memory
 
        // Fill the allocated memory st
        constructSTUtil(arr, 0, n - 1, 0);
    }
 
   
       
}

class Node{
	int a;
	int b;
	int c;
}

class MyComp implements Comparator<Node>{
    
	@Override
	public int compare(Node a,Node b) {
		
		// < == -1
		
		if(a.a < b.a){
			return -1;
		}else if(a.a > b.a){
			return 1;
		}else{
			return 0;
		}
		
		
	}
}