A peculiarity of the construction method given above for the odd magic squares is that the middle number ("n"2 + 1)/2 will always appear at the center cell of the magic square. Since there are ("n" - 1)! ways to arrange the skew diagonal terms, we can obtain ("n" - 1)! Greek squares this way; same with the Latin squares. Also, since each Greek square can be paired with ("n" - 1)! Latin squares, and since for each of Greek square the middle term may be arbitrarily placed in the main diagonal or the skew diagonal (and correspondingly along the skew diagonal or the main diagonal for the Latin squares), we can construct a total of 2 × ("n" - 1)! × ("n" - 1)! magic squares using this method. For "n" = 3, 5, and 7, this will give 8, 1152, and 1,036,800 different magic squares, respectively. Dividing by 8 to neglect equivalent squares due to rotation and reflections, we obtain 1, 144, and 129,600 essentially different magic squares, respectively.