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
imprakarsh:
20210212 14:43:36
1.No unary base is allowed(1111 != 4 its 15)


div_25:
20190528 16:00:50
We've got three things sure. What's the third thing again?


vishwanath_26:
20180630 20:10:00
Easy One! Take care of not using power function! 

Gowtham.R:
20150709 22:15:43
Finally After 5 WAs


devil:
20150702 00:26:41
brilliant question.....felt great after solving this one....!!! :) 

Anchrondite:
20150331 20:25:59
Do not even think to use pow function here got two wrong answers for me due to conversion between double and unsigned long long int . 

Bharath Reddy:
20140930 18:10:01
Read the "We are sure of three things.." part very very carefully 

Siya:
20140823 18:10:18
Very good problem ,Missing single point can leads to WA.. 

Flago:
20140227 16:34:41
I have no idea why my PHP give NZEC while it output the same as my C++, and run fine on ideone or in local. Maybe SPOJ doesn't support GMP functions ? Too bad, Limits could get much much higher :


Martijn Muijsers:
20131029 14:00:04
Oh dear... that is just SO incredibly evil. Getting this question right depends on reading the description VEEERY carefully. Damn you problem setter, you almost got me! Great prob :) 
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 