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.Linq;
using static System.Math;
using System.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        var n = long.Parse(Console.ReadLine().Trim());
        var a = getDiv(n);
        a.Remove(1);
        var a2 = check(n, a);
        var b = getDiv(n - 1);
        b.Remove(1);
        var hs = new HashSet<long>();
        foreach (var x in a2) hs.Add(x);
        foreach (var x in b) hs.Add(x);
        Console.WriteLine(hs.Count());
    }
    static List<long>  check (long n, List<long> a)
    {
        var ans = new List<long>();
        foreach (var x in a)
        {
            var t = n;
            while (true)
            {
                if (t % x == 0) t /= x;
                else break;
            }
            if (t % x == 1) ans.Add(x);
        }
        return ans;
    }
     static List<long> getDiv(long n)
    {
        var ans = new List<long>();
        for (int i = 1; i <= Sqrt(n); i++)
        {
            if (n % i == 0)
            {
                ans.Add(i);
                if (n != i * i) ans.Add(n / i);
            }
        }
        return ans;
    }
}