It can be shown that the Hill cipher with the matrix (a b c d) requires that (ad bc) is relatively prime to 26; that is the only common positive factor of (ad-bc) and 26 is 1. Thus, if (ad-bc) = 13 or is even, the matrix is not allowed. Determine the number of different (good) keys there are for a 2 x 2 Hill cipher without counting them one by one.