Problem
Once upon a time in a strange situation, people called a number ugly if it was divisible by any of the one-digit primes (2, 3, 5 or 7). Thus, 14 is ugly, but 13 is fine. 39 is ugly, but 121 is not. Note that 0 is ugly. Also note that negative numbers can also be ugly; -14 and -39 are examples of such numbers.
One day on your free time, you are gazing at a string of digits, something like:
123456
You are amused by how many possibilities there are if you are allowed to insert plus or minus signs between the digits. For example you can make
1 + 234 - 5 + 6 = 236
which is ugly. Or
123 + 4 - 56 = 71
which is not ugly.
It is easy to count the number of different ways you can play with the digits: Between each two adjacent digits you may choose put a plus sign, a minus sign, or nothing. Therefore, if you start with D digits there are 3D-1 expressions you can make.
Note that it is fine to have leading zeros for a number. If the string is "01023", then "01023", "0+1-02+3" and "01-023" are legal expressions.
Your task is simple: Among the 3D-1 expressions, count how many of them evaluate to an ugly number.
Input
The first line of the input file contains the number of cases, N. Each test case will be a single line containing a non-empty string of decimal digits.
Output
For each test case, you should output a line
Case #X: Y
where X is the case number, starting from 1, and Y is the number of expressions that evaluate to an ugly number.
Limits
Time limit: 30 5 seconds per test set.
Memory limit: 1GB.
0 ≤ N ≤ 100.
The string in each test case will be non-empty and will contain only characters '0' through '9'.
Small dataset (Test set 1 - Visible; 10 Points)
Each string is no more than 13 characters long.
Large dataset (Test set 2 - Hidden; 15 Points)
Each string is no more than 40 characters long.
Sample
4 1 9 011 12345
Case #1: 0 Case #2: 1 Case #3: 6 Case #4: 64