Devious Deck Derangement

The <<riffle shuffle>> is a common method for rearranging a deck of cards, performed by splitting the deck into two "packets" (ideally of equal size) and interleaving the cards from each. It matters which packet contributes a card first, so we'll specifically use an <<in shuffle>> such that the top and bottom cards do not retain their locations (as they would with an out shuffle). As an example, suppose we have a deck of six cards: Top half: {{1}} {{2}} {{3}} Bottom half: {{4}} {{5}} {{6}} Since the cards come out of the bottom of the packets, "dealing" from the bottom half first would result in the bottom card retaining its position; we don't want that, so we deal from the top half first and the new bottom card is the {{3}}. The {{6}} goes on top of that, then the {{2}}, the {{5}}, and so on, resulting in the following order: {{4}} {{1}} {{5}} {{2}} {{6}} {{3}}. After shuffling, it's common to <<cut>> the deck by swapping the top and bottom halves, which gives us: {{2}} {{6}} {{3}} {{4}} {{1}} {{5}}. The <<"derangement">> of a sequence is a measure of how out of order it is; for this problem, we'll use each card's distance from its original location (for instance, the {{6}} is 4 away from where it started) and the total derangement of the deck is the sum of these distances. That value is 10 with the current example deck, but we can do better; performing the shuffle-and-cut procedure once more increases the total derangement to 16. That is indeed the greatest possible value when starting with a deck of {{6}} cards, so we only had to perform the procedure {{2}} times. Given a deck of {{N}} distinct cards, how many times must it be <<shuffled-and-cut>> such that it is maximally deranged?