Pretty Song

题意翻译

## 题目描述 给你一个字符串，计算一下它的优美程度。 优美程度是指它的所有每一段连续子串优美程度的和。 优美程度的计算方法：这一段连续子串中I，E，A，O，U，Y的总数/字符串长度。 ## 输入格式 一串字符。 ## 输出格式 一个小数，表示该字符串的优美程度（误差不超过1e-6）。 ## 说明 在第一个样例中，所有的字母都是I，E，A，O，U，Y其中的一个。每个子串的优美程度为1。长度为7的字符串有28个连续子串。所以这个字符串的优美程度为28.

题目描述

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 $ .

输入输出格式

输入格式

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

输出格式

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

输入输出样例

输入样例 #1

IEAIAIO

输出样例 #1

28.0000000

输入样例 #2

BYOB

输出样例 #2

5.8333333

输入样例 #3

YISVOWEL

输出样例 #3

17.0500000

说明

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 $ .