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.

Examples

Input

6


Output

3


Input

3141


Output

13


Input

314159265358


Output

9
#include<bits/stdc++.h>
using namespace std;

typedef long long ll;

int main(){
	/*freopen("input.txt","r",stdin);
	freopen("output.txt","w",stdout);*/
	set<ll> s;
	ll n;
	cin>>n;
	if(n==2){
		cout<<1;
		return 0;
	}
	s.insert(n);
	s.insert(n-1);
	for(ll i=2;i*i<=n;i++){
		ll temp=n;
		while(temp%i==0) temp/=i;
		if(temp%i==1) s.insert(i);
		if((n-1)%i==0) s.insert((n-1)/i);
	}
	cout<<s.size();
	return 0;
}