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 (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func Scanner() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, 100000007)
	sc.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(Scanner())
	ans := 0
	for i := 1; i*i <= n; i++ {
		if (n-1)%i == 0 {
			if i*i == n-1 {
				ans += 1
			} else {
				ans += 2
			}
		} else if n%i == 0 && i != 1 {
			x := n
			for x%i == 0 {
				x /= i
			}
			if x%i == 1 {
				ans++
			}
			x = n
			j := n / i
			if i != j {
				for x%j == 0 {
					x /= j
				}
				if x%j == 1 {
					ans++
				}
			}
		}
	}
	fmt.Println(ans)
}