In a deck of $n > 1$ cards, some digits from $1$ to$8$are written on each card. A digit may occur more than once, but at most once on a certain card. On each card at least one digit is written, and no two cards are denoted by the same set of digits. Suppose that for every $k=1,2,\dots,7$ digits, the number of cards that contain at least one of them is even. Find $n$.