GCJ1C09A - All Your Base

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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 1018

1 ≤ the length of each line < 61

Sample


Input
 

Output
 
3
11001001
cats
zig
Case #1: 201
Case #2: 75
Case #3: 11

hide comments
Aditya Pande: 2013-10-25 08:50:19

This kind of output format has cost me so many WA's
Why not just print the number....
why?

metalbird: 2013-08-25 18:09:11

getting correct output for every input, still WA....! suggest any special test cases...

apsdehal: 2013-06-28 05:11:32

the question and its conditions should be carefully read Caused 4 WA's

raunakrocks: 2013-06-08 10:28:28

AC!! after many WA!!huh :P

(Tjandra Satria Gunawan)(曾毅昆): 2013-05-19 15:27:51

"We are sure of three things: the number is positive;"
Because I didn't read problem description carefully, I got 1 WA.. finally got AC :-)

fitcat: 2013-05-14 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.

Edit: Never mind. My stupid mistake.

Last edit: 2013-05-14 07:54:35

Added by:Shafaet
Date:2013-05-07
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