Flipping cards

You're given a deck of $99$ cards.

To perform one perfect shuffle, you divide the deck into three parts: the top $33$ cards, middle $33$ cards, and the bottom $33$ cards. Call these ${ P }_{ 1 }$ , ${ P }_{ 2 }$ , and ${ P }_{ 3 }$ respectively.

To finish the perfect shuffle, you choose a card from the top of ${ P }_{ 3 }$ and make it the first card in a new pile. Then, take a card from the top of ${ P }_{ 2 }$ and place it on top of the new pile, and so on. (This goes in a cycle, so once you get to ${ P }_{ 1 }$ you go back to ${ P }_{ 3 }$ )

How many perfect shuffles does it take to get back to the starting arrangement of cards?