A. Filling Shapes
dp; math
You have a given integer \(n\). Find the number of ways to fill all \(3 \times n\) tiles with the shape described in the picture below. Upon filling, no empty spaces are allowed. Shapes cannot overlap. This picture describes when \(n = 4\). The left one is the shape and the right one is \(3 \times n\) tiles.
The only line contains one integer \(n\) (\(1 \le n \le 60\)) — the length.
Print the number of ways to fill.
In the first example, there are \(4\) possible cases of filling.In the second example, you cannot fill the shapes in \(3 \times 1\) tiles.