When printing text on paper we need ink. But not every character needs the same amount of ink to print: letters such as ’W’, ’M’ and ’8’ are more expensive than thinner letters as ’i’, ’c’ and ’1’. In this problem we will evaluate the cost of printing numbers in several bases.

As you know, numbers can be expressed in several different bases. Well known bases are binary (base2; digits 0 and 1), decimal (base 10; digits 0 to 9) and hexadecimal (base 16; digits 0 to 9 and letters A to F). For the general base n we will use the first n characters of the string\text{“0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ”}, which means the highest base in this problem is 36. The lowest base is of course 2.

Every character from this string has an associated cost, represented by an integer value between 1
and 128. The cost to print a number in a certain base is the sum of the costs of all characters needed
to represent that number. For the numbers given in the input, you will have to calculate the cheapest
base(s) to represent this number in. Numbers in any base are printed without leading zeros.

For every case in the input, print one line ‘Case X:’, without the quotes, where X is the case number starting from 1.

For every query within a case print one line \text{‘Cheapest base(s) for number Y :’} followed by the cheapest base(s) in increasing order, separated by one space. Y is the query in decimal format. Print a blank line between cases.

The numbers in the second sample output are actually all in one line just like the first sample output. Due to lack of horizontal space they are shown broken in two lines.