BY-MO 2000 Problem 3

Let $N \ge 5$ be given. Consider all sequences $(e_1,e_2,...,e_N)$ with each $e_i$ equal to $1$ or $-1$ . Per move one can choose any five consecutive terms and change their signs. Two sequences are said to be similar if one of them can be transformed into the other in finitely many moves. Find the maximum number of pairwise non-similar sequences of length $N$ .