The Improved Caesar Pig Latin Cipher The problem with the Caesar cipher is the resulting words are often unpronounceable.  The problem with Pig Latin is that it is easy to decode.  Why not combine them?  

Input

A word consisting of the 26 english letters.  

Output 

First, change every consonant in the word to the next consonant in the alphabet.  So, b goes to c, d goes to f, and z goes to b.  Then, change every vowel to the next vowel in the alphabet (u goes to a).  Last, only if the first letter of the word is a consonant, move that letter to the end of the word and add "ay" to the end of the word.  

Examples:

cat -&gt; evday  
dog -&gt; uhfay   
eel -&gt; iim



This is code-golf, so the shortest code wins.
Case does not matter. 
Vowels that will be used are A, E, I, O, and U
Ruby, 96 69 bytes



-&gt;s{/^[^aeiou]/=~(r=s.tr'zb-yadehinotu','b-zefijopuva')?$'+$&amp;+'ay':r}


Try it online!

Fun fact of the day: tr() matches strings right-to-left. I always assumed it was left-to-right.