<image> As shown in the figure, if a second square ACEF is constructed with the diagonal AC of the square ABCD as its side, and a third square AEGH is constructed with the diagonal AE of the square ACEF as its side, and so on..., given that the area of the square ABCD, S_{1}, is 1, the areas of the subsequent squares constructed in the described manner are S_{2}, S_{3}, ..., S_{n} (where n is a positive integer). Then the area of the 8th square S_{8}=(___ ), and S_{n}=(___ ).