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.Collections;
using System.Linq;

namespace Atcoder_0403
{
    class Program
    {
        static void Main(string[] args)
        {
            long _targetNumber = GetInput_long()[0];
            HashSet<long> _yakusuSet=new HashSet<long>();
            HashSet<long> _resultSet=new HashSet<long>();

            //Nの約数を取得
            for (long i = 2; i * i <= _targetNumber; i++)
            {
                if (_targetNumber % i == 0)
                {
                    _yakusuSet.Add(i);
                    _yakusuSet.Add(_targetNumber / i);
                }
            }
            //Nの約数についての検証
            foreach(var data in _yakusuSet)
            {
                long temp = _targetNumber;
                while (temp % data == 0)
                {
                    temp /= data;
                }
                if (temp % data == 1)
                {
                    _resultSet.Add(data);
                }
            }
            //Nの約数でない場合についての検証
            for(long i = 2; i * i <= _targetNumber - 1; i++)
            {
                if ((_targetNumber-1) % i == 0)
                {
                    _resultSet.Add(i);
                    _resultSet.Add((_targetNumber-1)/i);
                }
            }
            _resultSet.Add(_targetNumber);
            if(_targetNumber-1>1)_resultSet.Add(_targetNumber-1);
            Console.WriteLine(_resultSet.Count);
        }

        #region input


        static string[] GetInput_string()
        {
            var input = Console.ReadLine().Split(' ');
            return input;
        }

        static int[] GetInput_int()
        {
            var input = GetInput_string();
            var result = new int[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = int.Parse(input[i]);
            }
            return result;
        }
        static long[] GetInput_long()
        {
            var input = GetInput_string();
            var result = new long[input.Length];
            for (int i = 0; i < result.Length; i++)
            {
                result[i] = long.Parse(input[i]);
            }
            return result;
        }
        #endregion
        #region sonota
        static void Swap_array<T>(T[] target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        static void Swap_list<T>(List<T> target, int a, int b)
        {
            T temp = target[a];
            target[a] = target[b];
            target[b] = temp;
        }
        #endregion
    }
}