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 Perl (v5.18.2) (judge verdict: Wrong Answer)

$N = <STDIN>;
chomp $N;
#print "$N\n";
if($N==2){print "1";exit}

my $count =2;#NとN-1

for(my $i=2;$i<=sqrt($N);$i++){
    $task =&ch($i,$N);
    #print "i$i $task\n";
    if( $task ==1){
        $count++;
    }
}
for(my $i=2;$i<=sqrt($N-1);$i++){
    my $mod = ($N-1)%$i;
    if( $mod == 0){
        $count++;
    }
}

print "$count\n";

sub ch {
    my ($a,$b) = @_;
    #print "ch $a $b\n";
    my $mod = $b%$a;
    if( $mod == 0){
        $ans = &ch($a,($b/$a));
        return $ans;
    }else{
      return $mod;
    }
}