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"

class Integer
  def divisors
    prime_division.inject([1]) do |ary, (p, e)|
      (0..e).map{ |e1| p ** e1 }.product(ary).map{ |a, b| a * b }
    end.sort
  end
end

n = gets.to_i

ans = (n-1).divisors.size - 1

n.divisors.each do |d|
  next if d == 1
  t = n
  while t % d == 0 do
    t /= d
  end
  ans += 1 if t % d == 1
end

puts ans