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:

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The prettiness of s equals 

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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.*;
 
	 
	 
	public   class Main {
		private InputStream is;
		private PrintWriter out;
		int time = 0, val[][], dp[][], DP[], start[], end[], dist[],  black[], MOD = (int)(1e9+7), arr[], weight[][], x[], y[], parent[];
		int MAX = 800000, N, K;
		long red[];
		ArrayList<Integer>[] amp;
		ArrayList<Pair>[][] pmp;
		boolean b[], boo[][];
		Pair prr[];
		HashMap<Integer,Long> hm[] = new HashMap[305];
		long Dp[][][][] = new long[110][110][12][12];
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			//out.close();
			out.flush();
			//tr(System.currentTimeMillis() - s + "ms");
		}
		public static void main(String[] args) throws Exception {
			new Thread(null, new Runnable() {
			public void run() {
				try {
			//new CODEFORCES().soln();
			} catch (Exception e) {
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			new Main().soln();
		}
		int ans = 0, cost = 0;
		char ch[], ch1[];
		void solve(){
			char ch[] = ns().toCharArray();
			int n = ch.length;
			int arr[] = new int[n+2];
			long sum[] = new long[n+2];
			int cnt = 0;
			for(int i = 0;i<n/2;i++){
				arr[i+1] = arr[i];
				if(ch[i]=='A' || ch[i]=='E' || ch[i]=='I' || ch[i]=='O' || ch[i]=='U' || ch[i]=='Y'){
					arr[i+1]++;
					cnt++;
				}
				sum[i+1] = sum[i]+arr[i+1];
			}
			for(int i = n-1; i>=n/2; i--){
				arr[i+1] = arr[i+2];
				if(ch[i]=='A' || ch[i]=='E' || ch[i]=='I' || ch[i]=='O' || ch[i]=='U' || ch[i]=='Y'){
					arr[i+1]++;
					cnt++;
				}
				sum[i+1] = sum[i+2]+arr[i+1];
			}
			double ans = 0;
			long val[] = new long[n+1];
			int j = 0;
			//System.out.println(cnt);
			for(int i = n;i>(n)/2;i--){
				long temp = cnt*1l*(n-i+1);
				temp -= (sum[j]+sum[n+1-j]);
				j++;
				val[i] = temp;
			}
			for(int i = 1;i<=n/2;i++){
				val[i] = val[n+1-i];
			}
			for(int i = 1;i<=n;i++){
			//	System.out.print(val[i] +" ");
				ans += (val[i]/(double)(i));
			}
			//System.out.println();
			System.out.println(ans);
		}
		void sieve(int n){
			b = new boolean[n+1];
			b[0] = b[1] = true;
			for(int i = 2;i*i<n;i++){
				if(!b[i]){
					for(int j = 2*i;j<100001;j+=i) b[j] = true;
				}
			}
		}
		class Pair implements Comparable<Pair>{
			int u, v, i;
			
			Pair(int u, int v){
				this.u = u;
				this.v = v;
			}
			Pair(){
				
			}
			Pair(int u, int v, int i){
				this.u = u;
				this.v = v;
				this.i = i;
			}
			public int hashCode() {
				return Objects.hash();
			}
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v)); 
			}
			public int compareTo(Pair other) {
				//return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v,other.v));
			}
			public String toString(){
				return this.u +" " + this.v;
			}
		}
		int max(int a, int b){
			if(a>b) return a;
			return b;
		}
		public static class FenwickTree {
			
		    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	 
		    public FenwickTree(int size) {
		        array = new int[size + 1];
		    }
		    public int rsq(int ind) {
		        assert ind > 0;
		        int sum = 0;
		        while (ind > 0) {
		            sum += array[ind];
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
		            ind -= ind & (-ind);
		        }
		        return sum;
		    }
		    public int rsq(int a, int b) {
		        assert b >= a && a > 0 && b > 0;
		        return rsq(b) - rsq(a - 1);
		    }
		    public void update(int ind, int value) {
		        assert ind > 0;
		        while (ind < array.length) {
		            array[ind] += value;
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
		            ind += ind & (-ind);
		        }
		    }
		    public int size() {
		        return array.length - 1;
		    }
		}
		void buildGraph(int n){
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		public int gcd(int a, int b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		static class ST1{
			int arr[], st[], size;
			ST1(int a[]){
				arr = a.clone();
				size = 10*arr.length;
				st = new int[size];
				build(0,arr.length-1,1);
			}
			void build(int ss, int se, int si){
				if(ss==se){
					st[si] = arr[ss];
					return;
				}
				int mid = (ss+se)/2;
				int val = 2*si;
				build(ss,mid,val); build(mid+1,se,val+1);
				st[si] = Math.min(st[val], st[val+1]);
			}
			int get(int ss, int se, int l, int r, int si){
				if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
				if(l<=ss && r>=se) return st[si];
				int mid = (ss+se)/2;
				int val = 2*si;
				return Math.min(get(ss,mid,l,r,val), get(mid+1,se,l,r,val+1));
			}
		}
		static class ST{
			int arr[],lazy[],n;
			ST(int a){
				n = a;
				arr = new int[10*n];
				lazy = new int[10*n];
			}
			void up(int l,int r,int val){
				update(0,n-1,0,l,r,val);
			}
			void update(int l,int r,int c,int x,int y,int val){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l>r||x>y||l>y||x>r)
					return;
				if(x<=l&&y>=r){
					lazy[c]+=val;
					return ;
				}
				int mid = l+r>>1;
				update(l,mid,2*c+1,x,y,val);
				update(mid+1,r,2*c+2,x,y,val);
				arr[c] = Math.max(arr[2*c+1], arr[2*c+2]);
			}
			int an(int ind){
				return ans(0,n-1,0,ind);
			}
			int ans(int l,int r,int c,int ind){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l==r)
					return arr[c];
				int mid = l+r>>1;
				if(mid>=ind)
					return ans(l,mid,2*c+1,ind);
				return ans(mid+1,r,2*c+2,ind);
			}
		}
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
	 
	 
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}