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 PHP (7.4.4) (judge verdict: Accepted)

<?php
$N = (int)fgets(STDIN);

if ($N === 2) {
    echo 1;
    return;
}

$ans = 2;
for ($K = 2; $K <= (int)sqrt($N) ;$K++) {
    if (($N - 1) % $K === 0) {
        $ans += 1;
        if ($K * $K !== $N - 1) {
            $ans += 1;
        }
        continue;
    }
    $n = $N;
    while ($n % $K === 0) {
        $n = $n / $K;
    }
    if ($n % $K === 1) {
        $ans += 1;
    }
}

echo $ans;