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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define rep1(i,n) for(int i=1;i<=(int)n;i++)
#define rep2(i,j,n) for(int j=i;j<n;j++)
#define rep3(i,j,n) for(int j=i;j<=n;j++)
#define rrep(i,n) for(int i=n-1;i>=0;i--)
#define sp(n) cout << fixed << setprecision(n)
typedef long long ll;
using namespace std;
int main(void){
    ll n;cin>>n;
    ll a=n-1;
    ll res=1;
    for(int i=2;i<=sqrt(a);i++){
        ll cnt=1;
        while(a%i==0){
            cnt++;
            a/=i;
        }
        res*=cnt;
    }
    if(a>=2)res*=2;
    for(int i=2;i<=sqrt(n);i++){
        a=n;
        while(a%i==0)a/=i;
        a%=i;
        if(a==1)res++;
    }
    
    cout<<res<<endl;
}