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>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define mk make_pair
#define fi first
#define se second
#define vll vector<ll>
#define pii pair<ll,ll>
#define vvll vector< vector<ll> >
#define pb push_back
#define sz(v) (v).size()
#define inf 1e18
#define md 998244353
#define all(v) (v).rbegin(),(v).rend()
#define rep(i,a,b) for(ll i=a;i<b;++i)
#define tel(a){cout<<a<<"\n";}
#define tell(a,b){cout<<a<<" | "<<b<<"\n";}
#define telll(a,b,c){cout<<a<<" | "<<b<<" | "<<c<<"\n";}
#define teln(v,n){cout<<"v- ";rep(i,0,n)cout<<v[i]<<" ";cout<<"\n";}
#define IOS ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define tihs if(fopen("inp.txt","r"))freopen("inp.txt", "r", stdin),freopen("out.txt", "w", stdout);
using namespace std;
#define TRACE
 
#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}
#else
#define trace(...)
#endif
 

#define M 200010

// (n-1)/m=k
int main(){
	IOS;
	tihs;

	ll n;cin>>n;n--;
	ll ans=1,x=n-1;
	for(ll i=2;i*i<=x;++i){
		if(n%i==0){
			ll p=i,c=0;
			while(n%p==0)n/=p,c++;
			ans*=(c+1);
		}
	}
	if(n>1)ans*=2;
	cout<<ans+1;

	return 0;
}