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>
#define ll long long
using namespace std;
int main()
{
	ll n;
	cin>>n;
	int ans=1;
	for(ll i=2;i*i<=n;i++){
		if(n%i==0){
			ll t=n;
			while(t%i==0){
				t/=i;
			}
			if((t-1)%i==0){
				ans++;
			}
			t=n;
			if(i*i==n)continue;
			ll x=n/i;
			while(t%x==0){
				t/=x;
			}
			if((t-1)%x==0){
				ans++;
			}
		}
	}
	n--;
	if(n>1)ans++;
	for(ll i=2;i*i<=n;i++){
		if(n%i==0){
			ans+=2;
			if(i*i==n)ans--; 
		}
	}
	cout<<ans;
}