A9864 | Pretty Song

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 $s_{i}$ 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 $I,E,A,O,U,Y$ .

The input contains a single string $s$ ( $1<=|s|<=5·10^{5}$ ) — the title of the song.

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