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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"fmt"
	"sort"
)

func main() {
	var n int
	fmt.Scan(&n)

	res := solve(n)
	ans := len(res)
	fmt.Println(ans)
}

func solve(n int) []int {
	var res []int

	divs1 := divisors(n - 1)
	res = divs1[1:]

	divs := divisors(n)
	for _, k := range divs {
		if k == 1 {
			continue
		}
		m := n
		for m%k == 0 {
			m /= k
		}
		if m%k == 1 {
			res = append(res, k)
		}
	}
	sort.Ints(res)

	return res
}

func divisors(n int) []int {
	res := make([]int, 0)
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			res = append(res, i)
			if n/i != i {
				res = append(res, n/i)
			}
		}
	}
	sort.Ints(res)

	return res
}