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.