CF509E.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.

当萨沙上七年级时，他开始大量听音乐。为了评估自己更喜欢哪些歌曲，他引入了“歌曲优美度”的概念。歌曲的标题是一个仅由大写拉丁字母组成的单词，而歌曲的优美度即为其标题的优美度。

我们定义一个单词的简单优美度为：该单词中元音字母的个数与单词总字母个数之比。

我们定义一个单词的优美度为：该单词所有子串的简单优美度之和。

更形式化地，定义函数 $\text{vowel}(c)$：若 $c$ 是元音，则 $\text{vowel}(c) = 1$；否则 $\text{vowel}(c) = 0$。设 $s_i$ 表示字符串 $s$ 的第 $i$ 个字符，$s_{i..j}$ 表示字符串 $s$ 中从第 $i$ 个字符开始、到第 $j$ 个字符结束的子串（即 $s_i s_{i+1} \dots s_j$，其中 $i \leq j$）。

则 $s$ 的简单优美度定义为如下公式：

$s$ 的优美度等于：

请计算给定歌曲标题的优美度。

我们约定元音字母为：I, E, A, O, U, Y。

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

输入包含一个字符串 $s$（$1 \leq |s| \leq 5\cdot10^5$）——歌曲的标题。

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

以绝对或相对误差不超过 $10^{-6}$ 输出该歌曲的优美度。

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.

在第一个样例中，所有字母均为元音字母。每个子串的简单优美度均为 1。长度为 7 的单词共有 28 个子串。因此，该歌曲的优美度等于 28。