Winnie has a deck of 8 cards where each card has a number from 1 to 4, inclusive, and each number appears twice in the deck. One at a time, Winnie reveals the top card and places it on the table. If two cards have matching numbers, she removes both of them from the table before revealing the next card. Of the 8! possible orderings of the deck, find the number of orderings such that there is never more than two distinct numbers on the table at a time.