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| 2 the 9s | |
| A well-known trick to know if an integer N is a multiple of nine is to compute the sum S of its digits. | |
| If S is a multiple of nine, then so is N. This is a recursive test, and the depth of the recursion needed | |
| to obtain the answer on N is called the 9-degree of N. | |
| Your job is, given a positive number N, determine if it is a multiple of nine and, if it is, its 9-degree. | |
| Input | |
| The input is a file such that each line contains a positive number. A line containing the number 0 is | |
| the end of the input. The given numbers can contain up to 1000 digits. | |
| Output | |
| The output of the program shall indicate, for each input number, if it is a multiple of nine, and in case | |
| it is, the value of its nine-degree. See the sample output for an example of the expected formatting of | |
| the output. | |
| Sample Input | |
| 999999999999999999999 | |
| 9 | |
| 9999999999999999999999999999998 | |
| 0 | |
| Sample Output | |
| 999999999999999999999 is a multiple of 9 and has 9-degree 3. | |
| 9 is a multiple of 9 and has 9-degree 1. | |
| 9999999999999999999999999999998 is not a multiple of 9. |