GCJ1C09A  All Your Base
Problem
In A.D. 2100, aliens came to Earth. They wrote a message in a cryptic language, and next to it they wrote a series of symbols. We've come to the conclusion that the symbols indicate a number: the number of seconds before war begins!
Unfortunately we have no idea what each symbol means. We've decided that each symbol indicates one digit, but we aren't sure what each digit means or what base the aliens are using. For example, if they wrote "ab2ac999", they could have meant "31536000" in base 10  exactly one year  or they could have meant "12314555" in base 6  398951 seconds, or about four and a half days. We are sure of three things: the number is positive; like us, the aliens will never start a number with a zero; and they aren't using unary (base 1).
Your job is to determine the minimum possible number of seconds before war begins.
Input
The first line of input contains a single integer, T. T test cases follow. Each test case is a string on a line by itself. The line will contain only characters in the 'a' to 'z' and '0' to '9' ranges (with no spaces and no punctuation), representing the message the aliens left us. The test cases are independent, and can be in different bases with the symbols meaning different things.
Output
For each test case, output a line in the following format:
Case #X: V
Where X is the case number (starting from 1) and V is the minimum number of seconds before war begins.
Limits
1 ≤ T ≤ 100
The answer will never exceed 10^{18}
1 ≤ the length of each line < 61
Sample
Input 
Output 
3 
Case #1: 201 
hide comments
Aditya Pande:
20131025 08:50:19
This kind of output format has cost me so many WA's


metalbird:
20130825 18:09:11
getting correct output for every input, still WA....! suggest any special test cases...


apsdehal:
20130628 05:11:32
the question and its conditions should be carefully read Caused 4 WA's 

raunakrocks:
20130608 10:28:28
AC!! after many WA!!huh :P 

(Tjandra Satria Gunawan)(æ›¾æ¯…æ˜†):
20130519 15:27:51
"We are sure of three things: the number is positive;"


fitcat:
20130514 05:31:43
Shafaet: The output of my program passed when submitted to the official site but got WA here. Would you please give me a hint? My submission id is 9258249.

Added by:  Shafaet 
Date:  20130507 
Time limit:  20s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Google Codejam 2009, Round 1C, Problem A 