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(){
	ll n;
	scanf("%lld",&n);
	if(n==2){
		printf("1");return 0;
	}
	long long ans=0;
	for(ll i=1;i*i<=n-1;i++){
        if((n-1)%i==0){
            if(i!=1)ans++;
            if((n-1)/i!=i)ans++;
        }
    }
	ans++;
	for(long long i=2;i*i<=n;i++){
		if(n%i==0){
			long long s=n;
			while(s%i==0) s/=i;
			if(s%i==1) ans++;
		}
	}
	printf("%lld",ans);
	return 0;
}