<image> A person designed a solo game with the following rules: A chess piece is initially placed at vertex A of a square ABCD (with a side length of 3 units) as shown in the figure. Then, a die is rolled to determine the number of units the piece should move counterclockwise along the edges of the square. If the number rolled is i (where i=1, 2, 3, 4, 5, 6), the piece moves i units counterclockwise. This process repeats continuously... The question is: After rolling the die three times, how many different ways are there for the piece to return to point A exactly?