Given a positive integer **n > 1** determine how many numbers can be made by adding integers greater than 1 whose product is **n**. For example if **n = 24** we can express **n** as a product in the following ways

```
24 = 24             -> 24            = 24
24 = 12 * 2         -> 12 + 2        = 14
24 = 6 * 2 * 2      -> 6 + 2 + 2     = 10
24 = 6 * 4          -> 6 + 4         = 10
24 = 3 * 2 * 2 * 2  -> 3 + 2 + 2 + 2 = 9
24 = 3 * 4 * 2      -> 3 + 4 + 2     = 9
24 = 3 * 8          -> 3 + 8         = 11

```

We can get the following numbers this way:

```
24, 14, 11, 10, 9

```

That is a total of 5 numbers, so our result is 5.

Task
====

Write a program or function that takes **n** as input and returns the number of results that can be obtained this way.

This is a [code-golf](/questions/tagged/code-golf "show questions tagged 'code-golf'") question so answers will be scored in bytes, with fewer bytes being better.

OEIS sequence
-------------

[OEIS A069016](https://oeis.org/A069016)