Tri Tiling

/problems/tritiling/file/statement/en/img-0001.jpg

In how many ways can you tile a $3\times n$ rectangle with $2\times 1$ dominoes?

Here is a sample tiling of a $3\times 12$ rectangle.

\includegraphics{tiling}

Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer $0 \leq n \leq 30$. For each test case, output one integer number giving the number of possible tilings.

Sample Input 1 Sample Output 1
2
8
12
-1
3
153
2131