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

The input contains a single string $ s $ ( $ 1

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

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 $ .