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 Ruby (2.3.3) (judge verdict: Wrong Answer)

require 'prime'
n=gets.to_i
def f(n)
if n==2
1
elsif n==3
2
else
a=1
(n-1).prime_division.each{|x,e|
	a*=e+1
}
b=0
n.prime_division.map{|x,e|
b+=(1..e).count{|h|(n/x**h)%x==1}
}
a+b
end
end

def g(n)
(2..n).count{|k|
m=n
until m<k
if m%k==0
m=m/k
else
m-=k
end
end
m==1
}
end

p f(n)