Score : $600$ points
Given is a positive integer $N$.
We will choose an integer $K$ between $2$ and $N$ (inclusive), then we will repeat the operation below until $N$ becomes less than $K$.
In how many choices of $K$ will $N$ become $1$ in the end?
Input is given from Standard Input in the following format:
$N$
Print the number of choices of $K$ in which $N$ becomes $1$ in the end.
6
3
There are three choices of $K$ in which $N$ becomes $1$ in the end: $2$, $5$, and $6$.
In each of these choices, $N$ will change as follows:
3141
13
314159265358
9