Let n > 1 be an integer. We consider binary 2 n matrices, i.e., matrices with 2 rows and n columns, in which each entry is 0 or 1. Any column in such a matrix is of one of four types, based on the bits that occur in this column. We will refer to these types as 8-columns, -columns, columns, and columns. For example, in the 2 7 matrix below, the first, second, and fifth columns are Q-columns, the third and seventh columns are -columns, the fourth column is a -con, and the sixth column is a -column 0 01 0 0 1 1 111 01 0 1 For the rest of this exercise, let k be an integer with 0