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A Different List Game
You are playing the following simple game with a friend:

The first player picks a positive integer $X$.

The second player gives a list of $k$ distinct positive integers $Y_1, \ldots , Y_ k$ such that $(Y_1+1)(Y_2+1) \cdots (Y_ k+1) = X$, and gets $k$ points.
Write a program that plays the second player.
Input
The input consists of a single integer $X$ satisfying $10^3 \le X \le 10^{15}$, giving the number picked by the first player.
Output
Write a single integer $k$, giving the number of points obtained by the second player, assuming she plays as good as possible.
Sample Input 1  Sample Output 1 

1099511627776 
8 
Sample Input 2  Sample Output 2 

127381 
3 
CPU Time limit
2 seconds
Memory limit
1024 MB
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Author
Per Austrin
Source
Spotify Challenge 2010