PersistentNumber | Topcoder Archive

Problem Statement

Given a number x, we can define p(x) as the product of the digits of x. We can then form a sequence x, p(x), p(p(x))... The persistence of x is then defined as the index (0-based) of the first single digit number in the sequence. For example, using 99, we get the sequence 99, 9*9 = 81, 8*1 = 8. Thus, the persistence of 99 is 2. You will be given n, and you must return its persistence.

Definition

Class:: PersistentNumber
Method:: getPersistence
Parameters:: int
Returns:: int
Method signature:: int getPersistence(int n)
(be sure your method is public)

Constraints

n will be between 0 and 2,000,000,000, inclusive.

Examples

```
99
```
```
Returns: 2
```
The example from the problem statement.
```
268
```
```
Returns: 4
```
The sequence here is 268, 96, 54, 20, 0.
```
6
```
```
Returns: 0
```
6 is already a single-digit number.
```
68889789
```
```
Returns: 3
```
```
86898
```
```
Returns: 7
```

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