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: Wrong Answer)

n = gets.to_i

divs = lambda {|n|
  lim = Math.sqrt(n).floor
  fs = []
  1.upto(lim) do |k|
    if n % k == 0
      fs << k
      fs << n / k
    end
  end
  return fs
}

cnt = divs.call(n-1).size - 1

divs.call(n).each do |k|
  next if k == 1
  x = n
  while x % k == 0
    x /= k
  end

  if x % k == 1
    cnt += 1
  end
end

p cnt