Multiplicative persistence proposes that any number can be expressed as a single digit number by multiplying the digits of the number and keep following the process with the result until the process throws a single digit number.
You are to write a program that when given a number will show how many steps it will take to make a single digit number number via multiplicative persistence method.
Input
Input file contains N arbitary integer numbers in N lines.
Constraints:
0<=N<=10^18
The program should read until the end of file.
Dataset is huge. Usage of faster I/O is advised.
Output
Print the number of steps described above on new lines.
Sample
| Input | Output |
|---|---|
391 873 125 | 3 4 2 |
Explanation: Number given, 391. Step -1: 3 * 9 * 1 = 27 Step -2: 2 * 7 = 14 Step -3: 1 * 4 = 4 Thus the answer is 3 | |
Problem Setter: Niloy Sarker
