The Fibonacci word sequence of bit strings is defined as:
$$ F(n)=\begin{cases} 0 & n=0,\\ 1 & n=1,\\ F(n-1)+F(n-2) & n\ge 2. \end{cases} $$
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 $2^{63}$.
Examples
Input 1
6 10 7 10 6 01 6 101 96 10110101101101
Output 1
Case 1: 5 Case 2: 8 Case 3: 4 Case 4: 4 Case 5: 7540113804746346428