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.Text;

public class AtCoderF
{
    static void Main()
    {
        var sc = new Scanner();

        long n = sc.NextLong();

        long answer = 0;

        var divisors1 = GetDivisors(n);
        foreach (var div in divisors1)
        {
            if (div == 1)
            {
                continue;
            }
            long tmpN = n;
            while (true)
            {
                if (tmpN % div == 0)
                {
                    tmpN /= div;
                }
                else
                {
                    break;
                }
            }
            if (tmpN % div == 1)
            {
                answer++;
            }
        }

        var divisors2 = GetDivisors(n - 1);
        answer += divisors2.Count - 1;


        Console.WriteLine(answer);
    }

    private static List<long> GetDivisors(long n)
    {
        List<long> divisors = new List<long>();
        for (long i = 1; i * i <= n; i++)
        {
            if (n % i == 0)
            {
                divisors.Add(i);
                if (n / i != i)
                {
                    divisors.Add(n / i);
                }
            }
        }
        return divisors;
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}