We have n distinct cards laid out on a table in positions 1 through n. To shuffle the cards, we apply a function s to each card such that the card in position p is moved to position s(p). This function has the special property that no two cards get moved to the same position, and every position receives at least one card. Show that if we shuffle the cards twice, we can still be assured that no two cards get moved to the same position and every position receives at least one card. Define a function f that represents shuffling the cards twice and then prove f is bijective.