Problem
Once upon a time in a strange situation, people called a number ugly if it was divisible by any of the onedigit 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:
123456You 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 = 236which is ugly. Or
123 + 4  56 = 71which 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 3^{D1} expressions you can make.
Note that it is fine to have leading zeros for a number. If the string is "01023", then "01023", "0+102+3" and "01023" are legal expressions.
Your task is simple: Among the 3^{D1} 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 nonempty string of decimal digits.
Output
For each test case, you should output a line
Case #X: Ywhere X is the case number, starting from 1, and Y is the number of expressions that evaluate to an ugly number.
Limits
0 <= N <= 100.
The string in each test case will be nonempty and will contain only characters '0' through '9'.
Small dataset
Each string is no more than 13 characters long.
Large dataset
Each string is no more than 40 characters long.
Sample
Input 
Output 
4

Case #1: 0

Points  Correct  Attempted 

10pt  554  1040 
25pt  82  318 