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E. Pretty Song

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWhen 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 *s*_{i} be the *i*-th character of string *s*, and *s*_{i..j} be the substring of word *s*, staring at the *i*-th character and ending at the *j*-th character (*s*_{is}_{i + 1}... *s*_{j}, *i* ≤ *j*).

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

The prettiness of *s* equals

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*| ≤ 5·10^{5}) — 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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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