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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val N = nextLong()
    var ans = 0
    divisor(N).drop(1).forEach { x ->
        var w = N
        while (w % x == 0L) w /= x
        w %= x
        if (w == 1L) ans += 1
    }
    ans += divisor(N - 1).drop(1).size
    println(ans)
}

fun divisor(value: Long) = 
    (1 .. Math.sqrt(value.toDouble()).toLong())
        .filter { value % it == 0L }
        .map { listOf(it, value / it) }
        .flatten()
        .distinct()
        .sorted()

fun next() = readLine()!!
fun nextLong() = next().toLong()