Problem:
Score : 600 points

Problem Statement

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.

Operation: if K divides N, replace N with N/K; otherwise, replace N with N-K.

In how many choices of K will N become 1 in the end?

Constraints

2 \leq N \leq 10^{12}

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of choices of K in which N becomes 1 in the end.

Sample Input 1

6

Sample Output 1

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:

When K=2: 6 \to 3 \to 1

When K=5: 6 \to 1

When K=6: 6 \to 1

Sample Input 2

3141

Sample Output 2

13

Sample Input 3

314159265358

Sample Output 3

9

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)

main=do
 n<-readLn
 print$length$filter(f n)$(g n)++(g$n-1)
f n x
 |x==1=False
 |n`mod`x==0=f(n`div`x)x
 |otherwise=n`mod`x==1
g n=foldr f []$takeWhile((n>=).(^2))[1..n]
 where
  f i s
   |n`mod`i==0&&i*i<n=i:n`div`i:s
   |n`mod`i==0=i:s
   |otherwise=s