Write an F# function countshuffles n that counts how many calls to shuffle on a deck of n distinct "cards" it takes to put the deck back into its original order:

 > countshuffles 4;; val it : int = 2 

(To see that this result is correct, note that shuffle [1;2;3;4] = [1;3;2;4], and shuffle [1;3;2;4] = [1;2;3;4].) What is countshuffles 52?

Hint: Define an auxiliary function countaux(deck, target) that takes two lists and returns the number of shuffles it takes to make deck equal to target.