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, l, r) for(register int i = l; i < r; i++)
#define hrp(i, l, r) for(register int i = l; i <= r; i++)
#define rev(i, r, l) for(register int i = r; i >= l; i--)
#define D(x) cout<<"D: "<<#x<<'='<<x<<endl;
#define R(x, l) cout<<"R: Array "<<#x<<endl; rep(i, 0, l) cout<<' '<<i<<':'<<*(x+i)<<endl;
#define pb push_back
#define int ll
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
template<typename tn> inline tn next(void);
template<typename tn> inline ostream& operator << (ostream& os, const vector<tn>& v);
inline int max(int cnt, ...);
inline int min(int cnt, ...);
set<int> st;
signed main(void)
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n = next<int>();
	if (n == 2) cout<<2<<endl, exit(0);
	st.insert(n);
	st.insert(n-1);
	for(int i = 2; i*i <= n; i++)
	{
		int tmp = n;
		while(!(tmp)%i) tmp /= i;
		if (tmp%i == 1) st.insert(i);
		if (!((n-1)%i)) st.insert((n-1)/i);
	}
	cout<<st.size()+1<<endl;
	return 0;
}
template<typename tn> inline tn next(void)
{
	tn k;
	cin>>k;
	return k;
}
template<typename tn> inline ostream& operator << (ostream& os, const vector<tn>& v)
{
	rep(i, 0, v.size()) os<<v[i]<<' ';
	return os;
}
inline int max(int cnt, ...)
{
	int mx = -1e18;
	va_list l;
	va_start(l, cnt);
	while(cnt--) mx = max(mx, va_arg(l, int));
	va_end(l);
	return mx;
}
inline int min(int cnt, ...)
{
	int mn = 1e18;
	va_list l;
	va_start(l, cnt);
	while(cnt--) mn = min(mn, va_arg(l, int));
	va_end(l);
	return mn;
}