# Fibonacci Words

The Fibonacci word sequence of bit strings is defined as:

\begin{equation*} F(n) = \left\{ \begin{array}{ll} 0 & \text {if $n = 0$}\\ 1 & \text {if $n = 1$}\\ F(n-1) + F(n-2) & \text {if $n \ge 2$} \end{array}\right. \end{equation*}Here $+$ denotes concatenation of strings. The first few elements are:

$n$ |
$F(n)$ |

0 |
0 |

1 |
1 |

2 |
10 |

3 |
101 |

4 |
10110 |

5 |
10110101 |

6 |
1011010110110 |

7 |
101101011011010110101 |

8 |
1011010110110101101011011010110110 |

9 |
1011010110110101101011011010110110101101011011010110101 |

Given a bit pattern $p$ and a number $n$, how often does $p$ occur in $F(n)$?

## Input

The first line of each test case contains the integer $n$ ($0 \le n \le 100$). The second line contains the bit pattern $p$. The pattern $p$ is nonempty and has a length of at most $100\, 000$ characters.

## Output

For each test case, display its case number followed by the number of occurrences of the bit pattern $p$ in $F(n)$. Occurrences may overlap. The number of occurrences will be less than $\mathrm{2}^\mathrm {63}$.

Sample Input 1 | Sample Output 1 |
---|---|

6 10 7 10 6 01 6 101 96 10110101101101 |
Case 1: 5 Case 2: 8 Case 3: 4 Case 4: 4 Case 5: 7540113804746346428 |