| ## Page 1 | |
| 11005 | |
| Cheapest Base | |
| 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 (base | |
| 2; 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 “0123456789ABCDEFGHI- | |
| JKLMNOPQRSTUVWXYZ”, 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. | |
| Input | |
| The input has less than 25 test cases. The first line of input file denotes this number of test cases. The | |
| description of every test case is given below: | |
| The first 4 lines of every case contain 9 integers each: the costs of the 36 characters in the order | |
| given above. Then follows the number of queries on a line by itself. Every query appears on a line by | |
| itself and is formed by a number between 0 and 2000000000 in decimal format. | |
| Output | |
| 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 ‘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. | |
| Sample Input | |
| 2 | |
| 10 8 12 13 15 13 13 16 9 | |
| 11 18 24 21 23 23 23 13 15 | |
| 17 33 21 23 27 26 27 19 4 | |
| 22 18 30 30 24 16 26 21 21 | |
| 5 | |
| 98329921 | |
| 12345 | |
| 800348 | |
| 14 | |
| 873645 | |
| 1 1 1 1 1 1 1 1 1 | |
| 1 1 1 1 1 1 1 1 1 | |
| ## Page 2 | |
| 1 1 1 1 1 1 1 1 1 | |
| 1 1 1 1 1 1 1 1 1 | |
| 4 | |
| 0 | |
| 1 | |
| 10 | |
| 100 | |
| Sample Output | |
| Case 1: | |
| Cheapest base(s) for number 98329921: 24 | |
| Cheapest base(s) for number 12345: 13 31 | |
| Cheapest base(s) for number 800348: 31 | |
| Cheapest base(s) for number 14: 13 | |
| Cheapest base(s) for number 873645: 22 | |
| Case 2: | |
| Cheapest base(s) for number 0: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | |
| 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | |
| Cheapest base(s) for number 1: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | |
| 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | |
| Cheapest base(s) for number 10: 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | |
| 26 27 28 29 30 31 32 33 34 35 36 | |
| Cheapest base(s) for number 100: 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | |
| 26 27 28 29 30 31 32 33 34 35 36 |