Eli's Curious Experiment

Eli is a student who loves chemistry and recently joined a chemistry lab. There are $N$ test tubes in a row, numbered $1, 2, \dots, N$ from the left. Eli chooses some of the tubes and mixes them into one mixture. A mixture must satisfy both rules below.

1. Never choose two tubes whose numbers are adjacent.
2. No more tubes can be added without breaking rule 1. That is, every unchosen tube is adjacent to at least one chosen tube.

A choice of only one tube does not count as a mixture, so singletons are not counted.

For example, for $N = 5$ the valid mixtures are $\{1, 3, 5\}$, $\{2, 4\}$, $\{2, 5\}$, and $\{1, 4\}$, which is $4$ in total. $\{1, 3\}$ does not count because tube $5$ can still be added without breaking rule 1, so it violates rule 2.

For each given number $N$ of tubes, compute the number of different mixtures satisfying the rules.

The input consists of multiple test cases. Each test case is a single integer $N$ on its own line, with $1 \le N \le 76$. The last line contains a single $0$, which terminates the input and is not processed.

For each test case, in the order given, print one line. If the answer to the $k$-th test case is $A$, print Case #k: A. Every answer is smaller than $2^{31}$.