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"
)

func main() {
	var N int
	fmt.Scan(&N)
	m := make(map[int]bool)
	for _, div := range Divisors(N - 1) {
		m[div] = true
	}
	for _, div := range Divisors(N) {
		if div == 1 {
			continue
		}
		if m[div] {
			continue
		}
		x := N
		for x%div == 0 {
			x /= div
		}
		x %= div
		if x == 1 {
			m[div] = true
		}
	}
	m[2] = true
	m[N] = true
	delete(m, 1)
	fmt.Println(len(m))
}

func Divisors(n int) []int {
	nums := []int{}
	for i := 1; i*i <= n; i++ {
		if n%i == 0 {
			nums = append(nums, i)
			if i*i != n {
				nums = append(nums, n/i)
			}
		}
	}
	return nums
}