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)

n = gets.to_i

cnt = 0

for div in 1..([((n-1)**0.5).to_i, 10**6].min)
  if (n-1) % div == 0
    ns = [div, (n-1)/div].uniq
    ns.each{|num| cnt += 1 if num > 1}
  end
end

for div in 1..([(n**0.5).to_i, 10**6].min)
  if n % div == 0
    ns = [div, n/div].uniq
    ns.each do |num|
      if num > 1
        tmp = n
        while tmp % num == 0
          tmp /= num
        end
        cnt += 1 if tmp % num == 1
      end
    end
  end
end

puts cnt