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The Fibonacci word sequence of bit strings is defined as:

F(n) = 0 if n = 0; F(n) = 1 if n = 1; F(n) = F(n − 1) + F(n − 2) if n ≥ 2.

Here + denotes concatenation of strings. The first few elements are:

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 ≤ n ≤ 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 2⁶³.

Sample Input

6
10
7
10
6
01
6
101
96
10110101101101

Output for Sample Input

Case 1: 5
Case 2: 8
Case 3: 4
Case 4: 4
Case 5: 7540113804746346428