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: Time Limit Exceeded)

using System;
using System.Collections.Generic;

public class AtCoder_161_F
{
    public static void Main()
    {
        long nn = long.Parse(Console.ReadLine());
        List<long> ans = new List<long>();

        for (long k = 2; k <= nn; k++)
        {
            long n = nn;
            while (n % k == 0 && n > 1)
            {
                n /= k;
            }

            if ((n - 1) % k == 0)
            {
                ans.Add(k);
            }
        }

        Console.WriteLine(ans.Count);
    }
}