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 (2.7.1) (judge verdict: Accepted)

class Integer
  def divisor_list
    require 'prime'

    return [] if self <= 0
    return [1] if self == 1

    prime_division.map.with_index { |(base, k), i|
      s = i.zero? ? 0 : 1
      (s..k).map { |n| base ** n }
    }.inject { |res, e| res + res.flat_map { |t| e.map { |v| t * v } } }.sort
  end
end

N = gets.to_i

ans = 0

N.divisor_list.each do |k|
  next if k == 1

  n = N

  while n % k == 0
    n = n / k
  end

  ans += 1 if n % k == 1
end

ans += ((N - 1).divisor_list - [1]).size

puts ans