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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
class Program
{
    public static void Main()
    {
        long N = long.Parse(Console.ReadLine());
        var set = new HashSet<long> { N };
        if (N > 2) { set.Add(N - 1); }
        for (long i = 2; i * i <= N - 1; ++i)
        {
            if ((N - 1) % i == 0)
            {
                set.Add(i);
                if (i * i < N - 1) { set.Add((N - 1) / i); }
            }
        }
        for(long i = 2; i * i <= N; ++i)
        {
            long n = N;
            while (n % i == 0) { n /= i; }
            if (n % i == 1) { set.Add(i); }
        }
        Console.WriteLine(set.Count);
    }
}