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 N 1000005 
#define LL long long 
using namespace std;
bool check(LL n,LL K){
	while(n%K==0)n/=K;
	n%=K;
	return n==1;
}
int main(){
	LL n,ans=1;//K=n 
	cin>>n;
	for(LL i=2;i*i<=n;i++){
		if(n%i==0){
			if(check(n,i))ans++;
			if(i*i!=n&&check(n,n/i))ans++; 
		}
	}
	n--;
	for(LL i=1;i*i<=n;i++){
		 if(n%i==0){
		 	ans++;
		 	if(i*i!=n)ans++;
		 }
	}
	ans--;//K=1;
	cout<<ans<<endl; 
	return 0;
}