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

require 'prime'

nd = ->(n){n.prime_division.inject(1){|r, (_, e)| r * (e + 1)}}
ds = ->(n){n.prime_division.inject([1]){|a, (p, e)| (0 .. e).map{|k| p**k}.product(a).map{|x, y| x*y}} - [1]}
ans = nd[N - 1] - 1
ds[N].each do |k|
  n = N
  n /= k while n%k == 0
  ans += 1 if n%k == 1
end
puts ans