A binary string consists of ones and zeros. Given a binary string T , if there is no binary string S such that SSS (concatenate three copies of S together) is a substring of T, we say T is triple-free.
A pattern consists of ones, zeros and asterisks, where an asterisk(∗) can be replaced by either one or zero. For example, the pattern 0**1 contains strings 0001, 0011, 0101, 0111, but not 1001 or 0000.
Given a pattern P, how many triple-free binary strings does it contain? Input
Each line of the input represents a test case, which contains the length of pattern, n (0 < n < 31), and the pattern P. There can be maximum 35 test cases.
The input terminates when n = 0. Output
For each test case, print the case number and the answer, shown below.
Sample Input
4 0**1
5 *****
10 **01**01**
0
Sample Output
Case 1: 2
Case 2: 16
Case 3: 9