ProductOfDigits | Topcoder Archive

Problem Statement

You are given an int N. Find the smallest positive integer X such that the product of its digits (in decimal notation) is equal to N. Return the number of digits in X, or return -1 if such a number does not exist.

Definition

Class:: ProductOfDigits
Method:: smallestNumber
Parameters:: int
Returns:: int
Method signature:: int smallestNumber(int N)
(be sure your method is public)

Constraints

N will be between 1 and 1,000,000,000, inclusive.

Examples

```
1
```
```
Returns: 1
```
Just take X = 1. It contains 1 digit.
```
10
```
```
Returns: 2
```
Here the smallest possible X is 25.
```
26
```
```
Returns: -1
```
```
100
```
```
Returns: 3
```
The number 455 has 3 digits and the product of its digits is 4 * 5 * 5 = 100.
```
2520
```
```
Returns: 4
```
```
864
```
```
Returns: 4
```

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