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: Accepted)

require 'prime'

n = gets.to_i

# substraction only or `n` itself
m = Prime.prime_division(n-1).inject(1) { |z,(x,y)| z * (y+1) }

a = Prime.prime_division(n)

def f(ary, z, &block)
  return yield(z) if ary.empty?
  
  ary = ary.dup
  x, y = ary.pop
  (0..y).each do |i|
    f(ary, z * x**i, &block)
  end
end

f(a, 1) do |z|
  next if z <= 1 || z * z > n
  
  s, t = n, 0
  s, t = s.divmod(z) while t == 0
  
  m += 1 if t == 1
end

p m

load __FILE__ unless $stdin.eof?